This paper explores the controlled multi-networks of complex dynamical networks in which nodes are assumed to represent nonlinear dynamical systems. This multi-network systemic structure is assumed to be endowed by adequate communication networks in which, for study sake, the intra-node and the out-node inter-connections are distinguished. In turn, via multi-networks operating at control stabilized steady-state orbits (hidden isolated equilibrium or oscillation) of its node systems, possibly with faulty interconnections, certain confluence parallels between Siljak's coordinator and Chen's random-pinning supervisory controls emerge. Thus these findings are summarized in three novel propositions emphasizing their identical or similar roles. The supervisory control integrated complex multi-networks with locally stabilized nonlinear node dynamical systems emerge of paramount importance in the engineering cybernetics.

Nowadays, the popularity of chatbots, such as ChatGPT, has brought research attention to question answering systems, capable to generate natural language answers to user’s natural language queries. However, also in other kinds of systems, flexibility of querying, including but also going beyond the use of natural language, is an important feature. With this consideration in mind the paper presents a critical and comprehensive analysis of recent developments, trends and challenges of Flexible Query Answering Systems (FQASs). Flexible query answering is a multidisciplinary research field that is not limited to question answering in natural language, but comprises other query forms and interaction modalities, which aim to provide powerful means and techniques for better reflecting human preferences and intentions to retrieve relevant information. It adopts methods at the crossroad of several disciplines among which Information Retrieval (IR), databases, knowledge based systems, knowledge and data engineering, Natural Language Processing (NLP) and the semantic web may be mentioned. The analysis principles are inspired by the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) framework, characterized by a top-down process, starting with relevant keywords for the topic of interest to retrieve relevant articles from meta-sources And complementing these articles with other relevant articles from seed sources Identified by a bottom-up process. to mine the retrieved publication data a network analysis is performed Which allows to present in a synthetic way intrinsic topics of the selected publications. issues dealt with are related to query answering methods Both model-based and data-driven (the latter based on either machine learning or deep learning) And to their needs for explainability and fairness to deal with big data Notably by taking into account data veracity. conclusions point out trends and challenges to help better shaping the future of the FQAS field.

Data deduplication is of vital importance for mobile cloud computing to cope with the explosive growth of outsourced mobile data. In order to ensure the privacy of sensitive mobile data against an untrusted cloud, Message-Locked Encryption (MLE) has been proposed to enable deduplication over ciphertext. However, MLE prohibits data access control since it uses deterministic content-derived encryption keys. Recently, a lightweight rekeying-aware encrypted deduplication system (REED) has been proposed to achieve dynamic access control for secure data deduplication. However, REED is vulnerable to key-retaining attack and stub-retaining attack, which leads to insecure access revocation, and thus cannot support secure dynamic access control. In response, we present AC-Dedup, an encrypted deduplication storage system that supportssecure dynamic access controlfor mobile cloud storage. At the core of AC-Dedup are two novel encryption techniques namedmixed message locked encryptionandrandom stub re-encryptionto resist the two types of attacks, respectively. To the best of our knowledge, AC-Dedup is the first practical system that achieves secure data deduplication and secure dynamic access control simultaneously. We conduct security analysis and experimental evaluation on mobile device and cloud platform with real-world IoT datasets. The results show that AC-Dedup enables secure and efficient dynamic access control while preserving deduplication effectiveness.

Neural networks tend to suffer performance deterioration on previous tasks when they are applied to multiple tasks sequentially without access to previous data. The problem is commonly known as catastrophic forgetting, a significant challenge in continual learning (CL). To overcome the catastrophic forgetting, regularization-based CL methods construct a regularization-based term, which can be considered as the approximation loss function of previous tasks, to penalize the update of parameters. However, the rigorous theoretical analysis of regularization-based methods is limited. Therefore, we theoretically analyze the forgetting and the convergence properties of regularization-based methods. The theoretical results demonstrate that the upper bound of the forgetting has a relationship with the maximum eigenvalue of the Hessian matrix. Hence, to decrease the upper bound of the forgetting, we propose eiGenvalues ExplorAtion Regularization-based (GEAR) method, which explores the geometric properties of the approximation loss of prior tasks regarding the maximum eigenvalue. Extensive experimental results demonstrate that our method mitigates catastrophic forgetting and outperforms existing regularization-based methods.

Social choice function or voting procedure is one of the crucial concepts in the domain of political sciences.It maps individuals' preferences over a set of candidates to some subset (possibly one-element) of the candidates who can be thought as the winners of an election procedure.The paper is aimed at applications of formal concept analysis methods to study of social choice functions.We will construct concept lattices over selected set of social choice functions characterized by possessing some properties deemed as important from the point of view of political sciences.We will discuss issues connected with reducibility of both objects and attributes, irreducibility of object concepts as well as attribute concepts and attribute implications.We will discuss also the shape of the constructed concept lattice of social choice functions which in some part is exceptionally regular from the perspective of the lattice theory.

While making decisions its is often convenient to use Atanassov’s intuitionistic fuzzy sets (IFSs) which are a very suitable tool because they can express in a natural way a decision maker’s arguments and judgments for, against, and with hesitation. The IFSs attract much attention and find many applications though, obviously, there are still some conceptual and algorithmic open problems related to their use. One of such problems is the ranking of intuitionistic fuzzy alternatives. The problem is very important but not all known methods produce satisfactory results. In this paper, we recall and critically analyze several methods of ranking of the intuitionistic fuzzy alternatives. We analyze them from the point of view of the results they yield and compare them taking into account their very illustrative geometrical representations. It turns out that most of these methods, except for one, have similar geometrical representations. For this latter method, we augment the assumptions assumed in the original version with an additional assumption, a justified and natural one, though not explicitly included so far. We therefore obtain a clearer interpretation of formulas involved in the augmented version of the method since the arguments pro, against and the hesitation are explicitly accounted for. This transparency is relevant for the user because there is no intuitively appealing linear order among the intuitionistic fuzzy alternatives so that some additional assumptions are to be made while ranking the elements. These issues are dealt with, and examples are provided.

Two-stage fuzzy methodology for the optimal planning of selection of temporary logistics hubs (TLHs) is developed. At the first stage, a q-rung orthopair fuzzy TOPSIS approach is developed to form and present expert knowledge about opening temporary logistics hubs. Fuzzy TOPSIS-based approach allows to determine the order of opening of TLHs and to provide post-disaster decision-making. At the second stage, by help of the built fuzzy TOPSIS aggregation a new objective function is given. By use of the built criterion TLHs’ total identification level of the order of establishment can be maximized, and together with the criterion concerning minimization of the selected TLHs’ quantity, poses a multi-objective facility location set covering problem. The offered approach is demonstrated by the example of temporary logistics y. The analysis of the results obtained revealed the importance of taking into account the opinions of multiple decision-makers for ensuring coordination in service delivery in disaster region.

In recent years, natural disasters such as earthquakes, floods, tsunamis, tornadoes, and others have resulted in a significant increase in loss of life and material property. They can cause severe and lasting damage to countries. When the suitable candidate places of shelters' (Shelter Sites (SSs)) location are selected, a group of sites should be selected from them that in some sense better meet the requirements such as: maximizing the reliability index of the selection of shelters, minimizing costs, maximizing evacuation coverage, etc. Ensuring timely evacuation of victims from disaster-affected areas is one of the most important tasks of the emergency management system. We assume fuzziness in the facility location problems’ models, because there is insufficient amount of objective information on disaster region data. A fuzzy multi-objective emergency shelters’ location and victims’ evacuation problem (FMOESLVEP) in the disaster-stricken region is constructed. The model objectives include (1) maximizing the total selection reliability index of opened shelters; (2) minimizing overall costs, including fixed costs for opening shelters, transportation costs for victims, and maintenance costs, (3) minimizing monotonous waiting times for total evacuation of victims, and (4) minimizing the number of open shelters. Objective functions (1) and (3) are novel and their construction and study issues are one of the important tasks of this work.

The consequences of natural disasters have significantly increased the loss of human life and material damage in recent years. Such disasters as earthquakes, tsunamis, tornadoes and others can cause serious and lasting damage to regions and countries. Therefore, it is important to know how the transport fleets are organized and managed in the disaster areas, as it makes a crucial contribution to the efficiency of the relief distribution process. When the suitable places of distribution centers (DCs) are selected, a group of places should be selected from them that in some sense better meet the requirements such as: maximizing the reliability index of the selection of DCs, minimizing costs, maximizing demand coverage etc. Given the issues outlined in this study, we will consider a fuzzy multi-objective emergency location and vehicle routing problem (FMOELVRP). It is essential to allocate disaster affected areas and vehicles for DCs. It generates routes from DC to disaster-affected areas, taking into account distributed demand-supply. The purposes of the model are: (1) maximizing the total selection reliability index of opened DCs, (2) minimizing the fixed costs to establish DCs and the vehicle travelling cost, (3) minimizing the maximum travel time of the vehicle routes, and (4) maximizing the minimum possibilistic reliability of the routes for all service vehicles in the process. Objective functions of (1) and (4) are novel and their construction and study issues are one of the important tasks of this work. The input to the mathematical model of the system are objective data, as well as expert evaluations. The outputs of the system will solve the FMOELVRP for disasters’ zones. The Intelligent Support System for the FMOELVRP in disaster zones will be developed in our future research.

A group decision-making process is considered which is meant as that a group of experts (agents, decision-makers,…) rank a finite set of options from the best to the worst. A special class of such processes is discussed in which the number of experts is large or indeterminate, the so-called Large-Scale Group Decision-Making. In this type of process, a key factor is trust in making a decision and evaluating an alternative, and the problem of managing the trust of agents is in this type of process complex and challenging. In this paper, a new approach to the management of trust in a Large-Scale Group Decision-Making system is presented. For this purpose, clusters are formed based on two factors: the mutual trust that agents have for each other and the similarity of opinions. If these two conditions are met, the experts are grouped into a single cluster. In this way, it is possible to manage the trust of experts and to apply it to the formulation and solution of a Large-Scale Group Decision-Making system. It is also possible to detect isolated points, which are clusters of single experts.

A new class of group decision making model under fuzzy preferences and a fuzzy majority is proposed which combines the traditional, widely employed and successful decision (making) by consensus, and the new idea, based on recent results from decision and, cognitive sciences, management science, psychology, etc. suggesting that decision by consensus may often lead to noninnovative enough decisions, and a different approach based on individuals (agents) who are not consensory but express different, maybe dissensory opinions, with a higher innovation potential, may be better. Here, in the new model, after the first phase of traditional decision by consensus, we use the concepts of Kacprzyk and Zadrożny's [28] consensory and dissensory agents, and then use primarily testimonies of dissensory agents which can imply innovative options to be chosen by using Kacprzyk [17], [18], and Kacprzyk, Zadrożny, Fedrizzi and Nurmi [29] group decision solution concepts, notably various fuzzy cores (i.e. fuzzy sets of options preferred over most other options).

We propose here a new proposal for attribute selection in the models expressed by the intuitionistic fuzzy sets. We further develop our previous paper in which the approach was already extended and the first computational tests were performed, i.e., the method was compared with the Principal Component Analysis (PCA). Here we test how the method behaves in comparison with the selection while using the Gain Ratio. We consider classification problems and try to reduce the number of attributes to not obtain substantially worse results.

We propose a new approach to database querying, termed context seeking querying, which involves context that is crucial for information interpretation and understanding yet practically not considered in querying. We present a justification, formalization and two algorithms for the new queries.

Two similar approaches to the modeling of bipolar user preferences, namely bipolar queries (and their extension to contextual bipolar queries) and queries with relative object qualification, are presented from the point of view of a user-assisted database querying. Their close relation is discussed, similarities and differences highlighted and possible disadvantages for the user studied. Then a direct, practical comparison of both approaches supported by computational examples on a simplified, yet realistic data set is presented and discussed and possible implementation and usage recommendations are made.

In this paper we continue our previous considerations on attribute selection while a data set is expressed via an Atanassov's intuitionistic fuzzy set (IFS). We examine a simple, yet it seems, a powerful algorithm making use of the three term attribute description (membership values, non-membership values, and hesitation margins). We test the algorithm on the examples being well known benchmarks data from UCI Machine Learning Repository. The results are compared with one of the most used methods of model reduction, namely, the Principal Component Analysis.

A new approach to the use of fuzzy terms in analytic functions which constitute a standard part of the SQL syntax is proposed. The motivation is that though extensions of the SQL queries including linguistic (fuzzy) terms have been widely used as they have made it possible to better and more directly represent complex requirements of a human user searching a relational database, notably for generating linguistic summaries, there has been little attention paid so far to the use of analytic functions in this context. Analytic functions can provide for an attractive way of analysing data in a relational database and may be possibly adopted as a tool to generate even more sophisticated linguistic summaries. In this paper we study a basic structure of standard (crisp) analytic functions use and point out some opportunities to extend it using linguistic terms. A starting point for our discussion is the mechanism of grouping rows in SQL as it is one of the most important components of the application of analytic functions.

It is recognized that system trustworthiness is a hyperstructure embodied by the structural, behavioral, and system dimensions with a set of coherent attributes. We explore a theoretical framework of tripartite trustworthiness that can be applied to real-world autonomous systems. We present a formal study of the essences and mathematical models of system trustworthiness and their quantitative measurements in the contexts of autonomous and mission-critical intelligent systems where humans and machines interact in a hybrid environment.

We further develop, first, our compound query (cf. Kacprzyk and Zadrożny [20]) in which in a bipolar query (cf. Zadrożny and Kacprzyk [45]) the required and desired conditions, aggregated via "and possibly", are represented by queries with fuzzy linguistic quantifiers in the sense of Kacprzyk and Ziółkowski [23], followed by Kacprzyk, Zadrożny and Ziółkowski [24]. We consider in the bipolar query the context in the sense of Zadrożny, Kacprzyk and Dziedzic [46], [42], and employ our original approach to the dealing with data quality for the queries with fuzzy linguistic quantifiers (cf. Kacprzyk and Zadrożny [21]), and for the compound bipolar queries (Kacprzyk and Zadrożny [22]) to the case with the context. We use the aggregation via the OWA operators with importance.

Brain-Inspired Systems (BIS) are an emerging field of brain and intelligence sciences that studies natural intelligence models of AI and cognitive systems in one direction, and the formal models of the brain simulated by computational intelligence in another direction. A typical BIS is the cognitive robots that mimic and implement the brain through all cognitive levels. BIS provides insights for brain-machine interfaces (BMI), which may lead to novel man-machine interactions and hybrid intelligent systems. BIS may also advance classic computers from dada processors to the next generation of knowledge processors mimicking the brain. BIS will underpin a wide range of engineering paradigms such as cognitive systems, cognitive computers, cognitive robots, machine learning systems, semantic comprehension systems, big data systems, unmanned systems, self-driving vehicles and hybrid man-machine systems.

The Hamming distance is a well-known measure that is designed to provide insights into the similarity between two strings of information. In this study, we use the Hamming distance, the optimal deviation model, and the generalized ordered weighted logarithmic averaging (GOWLA) operator to develop the ordered weighted logarithmic averaging distance (OWLAD) operator and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. The main advantage of these operators is the possibility of modeling a wider range of complex representations of problems under the assumption of an ideal possibility. We study the main properties, alternative formulations, and families of the proposed operators. We analyze multiple classical measures to characterize the weighting vector and propose alternatives to deal with the logarithmic properties of the operators. Furthermore, we present generalizations of the operators, which are obtained by studying their weighting vectors and the lambda parameter. Finally, an illustrative example regarding innovation project management measurement is proposed, in which a multi-expert analysis and several of the newly introduced operators are utilized.

Human beings represent and process imperfect information in a natural way, whereas effective approaches are still being looked for in the area of soft computing. Atanassov's intuitionistic fuzzy sets and especially Atanassov's intuitionistic fuzzy relations are are tools that make it possible to model in an effective way imperfect information. In this paper, we discuss the transitivity problem of Atanassov's intuitionistic fuzzy relations. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making, choice, and utility theories widely making use of the preference procedures. We study here in detail transitivity property of Atanassov's intuitionistic fuzzy relations and propose a new algorithm for generating weakly transitivity among the alternatives (options) considered. Next, making use of the new algorithm we propose a procedure of ranking of the alternatives in a group decision-making problem.

With "human centric data management", we denote all kind of practical and theoretical developments that contribute to the improvement of data management for human users, such that it becomes better to understand, easier to handle, and more natural to communicate with.The popularity of digital applications, social media and multimedia created a shift towards "big data" that are characterized by huge data volumes, a large variety of data formats, fast data processing requirements, and veracity problems.The more data we have at our disposal, the more applications arise, but also the more sophisticated these applications become.Along with these technological developments comes the awareness that there is a growing need for human centric data management tools.Indeed, perfect data sets are rare and data imperfections propagate to imperfect data processing solutions.Humans communicate in natural language and cope with imperfect information in their everyday behavior, whereas conventional data management assumes that data are perfect and data manipulation is based on a bivalent Boolean logic.Computational intelligence techniques, more specifically soft computing and fuzzy set theory, offer the tools for bridging the gap between the way humans behave and communicate and the way conventional data management tools work.This is especially the case because they allow to generalize bivalent Boolean logic into multivalued fuzzy logic and offer sound foundations for uncertainty modeling that are less stringent, but broader applicable, than conventional probability theory.This special issue is an initiative of the working group on "Soft Computing in Database Management and Information Retrieval" of the European Society for

We further develop our concept of a compound query (cf. Kacprzyk and Zadroižny [23]) in which in a bipolar query comprising of a required and desired condition aggregated via a non-conventional operator corresponding to “and if possible” the particular required and desired conditions are by themselves queries with fuzzy linguistic quantifiers. We use our approach to the dealing with data quality (trustworthiness), originally developed for the queries with fuzzy linguistic quantifiers (cf. Kacprzyk and Zadrozny [25]), employ it for the required and desired conditions (queries with fuzzy linguistic quantifiers), and then implant into the compound query, i.e. a bipolar query with the required and desired conditions being queries with fuzzy linguistic quantifiers. A new conceptual quality, functionality and human consistency is therefore obtained.

We propose a novel approach to the moderator supported consensus reaching process in a group of agents. We assume the agents' testimonies to be fuzzy preference relations, a fuzzy majority, and the concept of a degree of consensus meant as the degree to which, e.g., most of important agents agree as to almost all of relevant options. We use to handle fuzzy majorities Zadeh's calculus of linguistically quantified propositions. We propose a new concept of a (fuzzy sets of) consensory and dissensory agents, and use our approach of using linguistic data summaries for a comprehensive summarization of how the agents' testimonies look like, separately for the consensory and dissensory agents to obtain a deeper view that can be useful for the moderator to suggest the agents changes of specific preferences that could lead to a higher degree of consensus. An explicit inclusion of opinions of the consensory and dissensory agents is a reflection of a fairness type attitude of the moderator as opinions of all agents are accounted for.

In the paper we revisit, and further analyze the concepts of two possible representations of Atanassov's intuitionistic fuzzy sets' (A-IFSs, for short): the two term one, in which the degrees of membership and non-membership are only involved, and the three term one, in which in addition to the above degrees of membership and non-membership the so called hesitation margin is explicitly accounted for. Though both representations are mathematically correct and may be considered equivalent, the second one involves explicitly an additional information. We show on examples of some decision making type problems its intuitive appeal and usefulness for reflecting more sophisticated intentions and preferences of the user.

A new type of linguistic summaries, so-called contextual linguistic summaries, are further developed. The point of departure are contextual bipolar queries which play the same role for a new type of summaries as flexible fuzzy queries do with respect to the classical linguistic summaries. The bipolar queries employed are of a special type, following the required/desired semantics formalized using the “and possibly” operator and a recently introduced “or, if impossible” operator. The latter is inspired by the work of Lietard et al. on another bipolarity related operator “or else”. The “or, if impossible” operator is its non truth functional counterpart, interpreted in the same vein as the “and possibly” operator employed and studied in our previous work. In the paper we extend the concept of contextual linguistic summaries using this new operator and study its basic properties as well as some more general properties of this class of summaries.

In this work we present a general memetic algorithm for solving a major robotic task, a Global Path Planning (GPP). It consists in finding a path (way) on an a-priori given map from a starting to a destination point. We are concerned with the solution of such a GPP problem for which a robot that has a non-holonomic kinematic structure and some movement constraints. A set of planning rules has been proposed together with a corresponding genotype improvement and repair methods. The presented numerical results presented confirm that the memetic algorithms can be a very promising tool for solving the Global Path Planning (GPP) problem.

We are concerned with the so-called bipolar database queries which are meant here as those in which the query is composed of a necessary and optional part connected with a non-conventional aggregation operator “and possibly” as, for instance, in the query “find houses in a database of a real estate agency which are cheap and possibly close to a railroad station”. We first analyse some foundational issues related to the bivariate unipolar scales employed, and various interpretations of the “and possibly” aggregation operator. We concentrate on its logical representation via various connectives known in multivalued (fuzzy) logic. We propose a novel concept of a hierarchical bipolar database query in which, basically, the original query is considered a level 0 query at the bottom of the precisiation hierarchy, then its necessary and optional parts are assumed to be bipolar queries themselves. This makes it possible to further precisiate the user's intentions/preferences. A level 1 of precisiation is obtained, and the process is continued as far as it is necessary for the user to adequately reflect his/her intentions/preferences as to what is sought.

We study the possibility to extend the concept of linguistic data summaries employing the notion of bipolarity. Yager's linguistic summaries may be derived using a fuzzy linguistic querying interface. We look for a similar analogy between bipolar queries and the extended form of linguistic summaries. The general concept of bipolar query, and its special interpretation are recalled, which turns out to be applicable to accomplish our goal. Some preliminary results are presented and possible directions of further research are pointed out.

This paper is a continuation and extension of our previous works on a correlation coefficient of Atanassov's intuitionistic fuzzy sets (A-IFSs). The correlation coefficient, an extension of Pearson's r which is one of the most frequently used tools in statistics, we have proposed provides the strength of the relationship between the A-IFSs and also shows if the considered sets are positively or negatively correlated. Moreover, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin. This concept is further dealt with. Moreover, what has not been done so far in the literature, an extended numerical analysis on the well known benchmarks of Pima and Iris data is provided.

We deal with the problem of how to evaluate the performance of an investment (mutual) fund, over a past period. We assume a widely assumed attitude that an investment fund is said to have performed well if its unit price have been rising faster than its benchmark during a period of growth, and has been falling slower than its benchmark during the period of decline. We develop a novel, flexible and human consistent comparison method that operates on the comparison of trends (segments) extracted from the times series representing the behavior of the fund and its benchmark. The result of comparison becomes a new data set that is linguistically summarized using the method proposed in our previous works.

When expressing their information needs in a (database) query, users sometimes prefer to state what has to be rejected rather than what has to be accepted. In general, what has to be rejected is not necessarily the complement of what has to be accepted. This phenomenon is commonly known as the heterogeneous bipolar nature of expressing information needs. Satisfaction degrees in regular fuzzy querying approaches are based on the “symmetric'' assumption that the extent to which a database record, respectively, satisfies and does not satisfy a given query are complements of each other and are therefore less suited to adequately handle heterogeneous bipolarity in query specifications and query processing. In this paper, we present a bipolar query satisfaction modeling framework which is based on pairs that consist of an independent degree of satisfaction and degree of dissatisfaction. The use and advantages of the framework are illustrated in the context of fuzzy query evaluation in regular relational databases. More specifically, the evaluation of heterogeneous bipolar queries that contain both positive, negative, and bipolar criteria is studied. © 2011 Wiley Periodicals, Inc.

We present a new approach to the evaluation of the similarity of time series. We consider, as in our previous works, the case of linguistic summarization of the past performance of an investment (mutual) fund and its underlying benchmark which is very important for an effective and efficient investment decision support. We propose a new comparison method based not on the comparison of the consecutive values or segments or trends of the fund and its benchmark but on linguistic summaries best describing their past behavior. Since our method derives a number of best linguistic summaries to be presented to the decision maker for consideration, we propose a new approach that boils down to the comparison of a set of linguistic summaries best describing the behavior of the fund and its benchmark, not just a pair of them. We take into account, as the measures of performance of the linguistic summaries of time series, the degree of truth and the degree of focus. The results obtained suggest that the new method proposed is very human consistent and intuitively appealing and may be relevant in the heavily human centered investment decision support task considered.

In this paper we address the problem of how to measure information conveyed by an Atanassov's intuitionistic fuzzy set (A-IFS for short) and a related concept of knowledge that is explicitly context oriented and useful from the point of view of a specific purpose, notably related to decision making. We pay particular attention to the relationship between the positive and negative information and a lack of information expressed by the hesitation margin.

A novel solution is proposed to an important problem of learning real querying preferences and intentions from users who need to retrieve interesting information from a database but are not in a position to specify their information needs and/or intentions using a query language due to lack of knowledge and/or experience. A solution is proposed that is based on the presentation to the user of consecutive examples of data items, requesting his/her evaluations of those data items, and then using a classification method to learn the user preferences to be converted into their corresponding query. A novel element is that the system proposed allows for both positive and negative responses from the user which makes possible to represent the bipolarity of preferences. The considerations are illustrated on an example of a querying system for a real estate agency that makes possible to retrieve houses from a database that more adequately reflects the users' intentions and preferences. A Web based implementation is briefly presented. Results obtained are promising.

We extend our previous work on the linguistic summarization of time series data meant as the linguistic summarization of trends, i.e. consecutive parts of the time series, which may be viewed as exhibiting a uniform behavior under an assumed (degree of) granulation, and identified with straight line segments of a piecewise linear approximation of the time series. We characterize the trends by the dynamics of change, duration, and variability. A linguistic summary of a time series is then viewed to be related to a linguistic quantifier driven aggregation of trends. We primarily employ for this purpose the classic Zadeh's calculus of linguistically quantified propositions, which is presumably the most straightforward and intuitively appealing, using the classic minimum operation and mentioning other t-norms. We also outline the use of the Sugeno and Choquet integrals proposed in our previous papers. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an 8-year period, by presenting first an analysis of characteristic features of quotations, under various (degrees of) granulations assumed, and then by listing some more interesting and useful summaries obtained. We propose a convenient presentation of linguistic summaries focused on some characteristic feature exemplified by what happens “almost always,” “very often,” “quite often,” “almost never,” etc. All these analyses are meant to provide means to support a human user to make decisions. © 2010 Wiley Periodicals, Inc.

We consider a consensus reaching process in a group of individuals meant as an attempt to make preferences of the individuals more and more similar, that is, getting closer and closer to consensus. We assume a general form of intuitionistic fuzzy preferences and a soft definition of consensus that is basically meant as an agreement of a considerable (e.g., most, almost all) majority of individuals in regards to a considerable majority of alternatives. The consensus reaching process is meant to be run by a moderator who tries to get the group of individuals closer and closer to consensus by argumentation, persuasion, etc. The moderator is to be supported by some additional information, exemplified by more detailed information on which individuals are critical as, for instance, they are willing to change their testimonies or are stubborn, which pairs of options make the reaching of consensus difficult, etc. In this paper we extend this paradigm proposed and employed in our former works with the use of a novel data mining tool, so called action rules which make it possible to more clearly indicate and suggest to the moderator with which experts and with respect to which option it may be expedient to deal. We show the usefulness of this new approach.

We point out some relevant issues that are related to the computing-with-words (CWW) paradigm and argue for an urgent need for a new, nontraditional look at the area, since the traditional approach has resulted in very valuable theoretical research results. However, there is no proper exposure and recognition in other areas to which CWW belongs and can really contribute, notably natural-language processing (NLP), in general, and natural-language understanding (NLU) and natural-language generation (NLG), in particular. First, we present crucial elements of CWW, in particular Zadeh's protoforms, and indicate their power and stress a need to develop new tools to handle more modalities. We argue that CWW also has a high implementation potential and present our approach to linguistic data(base) summaries, which is a very intuitive and human-consistent natural-language-based knowledge-discovery tool. Special emphasis is on the use of Zadeh's protoform (prototypical form) as a general form of a linguistic data summary. We present an extension of our interactive approach, which is based on fuzzy logic and fuzzy database queries, to implement such linguistic summaries. In the main part of the paper, we discuss a close relation between linguistic summarization in the sense considered and some basic ideas and solutions in NLG, thus analyzing possible common elements and an opportunity to use developed tools, as well as some inherent differences and difficulties. Notably, we indicate a close relation of linguistic summaries that are considered to be some type of an extended template-based, and even a simple phrase-based, NLG system and emphasize a possibility to use software that is available in these areas. An important conclusion is also an urgent need to develop new protoforms, thus going beyond the classical ones of Zadeh. For illustration, we present an implementation for a sales database in a computer retailer, thereby showing the power of linguistic summaries, as well as an urgent need for new types of protoforms. Although we use linguistic summaries throughout, our discussion is also valid for CWW in general. We hope that this paper—which presents our personal view and perspective that result from our long-time involvement in both theoretical work in broadly perceived CWW and real-world implementations—will trigger a discussion and research efforts to help find a way out of a strange situation in which, on one hand, one can clearly see that CWW is related to words (language) and computing and, hence, should be part of broadly perceived mainstream computational linguistics, which lack tools to handle imprecision. These tools can be provided by CWW. Yet, CWW is practically unknown to these communities and is not mentioned or cited, and---reciprocally---even the top people in CWW do not refer to the results that are obtained in these areas. We hope that our paper, for the benefit of both the areas, will help bridge this gap that results from a wrong and dangerous fragmentation of\break science.

Linguistic database summaries in the sense of Yager (1982), further extended to an implementable form by Kacprzyk & Yager (2001) and Kacprzyk, Yager & Zadrozny (2000), are extremely simple natural language like statements exemplified by, for a personnel database, “most employees are young and well paid” (with some degree of truth). They have been implemented in business contexts (cf. Kacprzyk & Zadrozny, ????, Kacprzyk, Wilbik and Zadrozny, 2006–2008). An effective and efficient way of their generation was proposed by Kacprzyk & Zadrozny (????) by using an interactive procedure based on Kacprzyk & Zadrozny's (????) fuzzy database queries with linguistic quantifiers. Moreover, in Kacprzyk & Zadrozny (???) the role of Zadeh's (???) protoform was shown and their use advocated. Though linguistic database summaries have a strong resemblance to natural language generation (NLG), this issue was never considered. In this paper we indicate some important issues that are common to linguistic database summarization and natural language generation, and propose some possible research directions.

We further extend our approach to the linguistic summarization of time series (cf. Kacprzyk, Wilbik and Zadrozny) in which an approach based on a calculus of linguistically quantified propositions is employed, and the essence of the problem is equated with a linguistic quantifier driven aggregation of partial scores (trends). In addition to the basic criterion of a degree of truth (validity), we also use as a degree of appropriateness as an additional quality criterion. However, for simplicity and tractability, we use in the first shot the degrees of truth (validity) and focus, which usually reduce the space of possible linguistic summaries to a considerable extent, and then - for a usually much smaller set of linguistic summaries obtained - we use the degree of appropriateness to make a final choice as it gives us an additional quality of being able to detect how surprising, i.e. valuable, a linguistic summary obtained is. We also mention relations to natural language generation (NLG) as pointed out recently by Kacprzyk and Zadrozny. We show an application to the absolute performance type analysis of daily quotations of an investment fund, and the numerical results are promising. The linguistic summaries obtained using this additional quality criterion of a degree of appropriateness seem to better reflect human intents and interest.

We discuss a conceptually new extension of our previous works in which we proposed a concept of a consensus reaching support system based on a new, gradual notion of consensus devised in the framework of fuzzy preference relations and a fuzzy majority. Here, first of all, we propose the use of action rules as a tool to generate some advice as to the further running of discussion in the group. Moreover, we propose to employ intuitionistic fuzzy preference relations to better model individual preferences and to obtain data more suitable for the action rules based analysis.

A fuzzy preference relation is a powerful and popular model to represent both individual and group preferences and can be a basis for decision-making models that in general provide as a result a subset of alternatives that can constitute an ultimate solution of a decision problem. To arrive at such a final solution individual and/or group choice rules may be employed. There is a wealth of such rules devised in the context of the classical, crisp preference relations. Originally, most of the popular group decision-making rules were conceived for classical (crisp) preference relations (orderings) and then extended to the traditional fuzzy preference relations. In this paper we pursue the path towards a universal representation of such choice rules that can provide an effective generalization—for the case of fuzzy preference relations—of the classical choice rules. © 2008 Wiley Periodicals, Inc.

Relevant contributions of fuzzy logic to the logical models in information retrieval is studied. It makes it possible to grasp the graduality of some relevant concepts and to model both imprecision and uncertainty inherent to the retrieval process, still in the framework of the broadly meant logical approach. In this perspective we discuss various extensions to the basic Boolean model which are needed to attain such a greater expressivity. In particular, we show how the well-known semantics of keywords weights may be recovered in various fuzzy logic based information retrieval models.

Taking as a point of departure our works on linguistic summarization of time series (cf. Kacprzyk, Wilbik and Zadrozny [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]) in which an approach based on a calculus of linguistically quantified propositions was proposed, and the essence of the problem was equated with a linguistic quantifier driven aggregation of partial scores (trends), we present here some reformulation and extension mainly towards a more complex evaluation of results resulting linguistic summaries obtained. We use the classic Zadehpsilas calculus of linguistically quantified propositions but, in addition to the basic criterion of a degree of truth (validity), we also use as the second criterion a degree of fuzziness to make it possible to account for a frequent case that though the degree of truth of a very general (not precise) summary is high, its usefulness may be low due to its high fuzziness. We show an application to the absolute performance type analysis of daily quotations of an investment fund.

In this paper we consider the problem of determining typical values. We heavily refer to some results of linguistic experiments in psychology and cognitive science. Since analyzes employed in those areas, which make use of some considerations on how an object is typical to a category and its related so called contrast category, we propose the use of Atanassovpsilas intuitionistic fuzzy sets (to be called A-IFSs, for short). We follow the line of reasoning known from psychology and cognitive sciences, in particular those resulting from linguistic experiments, and verify how those results work in the case of classification, an omnipresent problem in computer science, decision sciences, etc. Our considerations concentrate around a typical example discussed in cognitive sciences. We start from nominal data, i.e. names are assigned to objects as labels, and we investigate to which extent a linguistic representation in a psychological space succeeds in predicting categories via the intuitionistic fuzzy sets. We only consider here a model of categories with a geometrical centroid model in which the similarity is defined in terms of a distance to the centroids. Next, we verify if the extreme ideals, which are important in cognitive processes when categories are learnt in the presence of the alternative (contrast) category, give comparative results. We show that Atanassovpsilas intuitionistic fuzzy sets make it possible to reflect a positive and negative information via the concept of membership and non-membership. Though the paper presents an ongoing research, the first results obtained are promising and point out the usefulness and strength of Atanassovpsilas intuitionistic fuzzy sets as a tool to account for more aspects of vague data and information.

We show how Zadehpsilas calculus of linguistically quantified propositions can be applied to avoid duplicate names in a publication database of a research institute. This problem, in its most general form, is studied in the literature by various communities. Here we focus on a specific scenario in which a need for its solution arises. Moreover, we make an attempt to apply fuzzy logic based concepts to solve it. The approach proposed yields promising results for the data for which it has been initially conceived and seems to be applicable also in a more general context. Its primary advantage is the ease and intuitiveness of customization. The main parameters take the form of linguistic quantifiers whose meaning is arguably familiar for an average user and which are fairly easy to be tuned to the changing requirements.

Linguistic summaries as descriptions of trends in time series data are proposed. We further extend our (cf. Kacprzyk, Wilbik and Zadrozny, 2006) previous works in which we put forward a new approach to the linguistic summarization of time series. In this paper we basically propose a modification of our previous work on the use of the Sugeno integral developed in 2006 by employing a modified fuzzy measure and its related modified Sugeno integral. This gives better results in particular in the case of some more sophisticated and extended types of summaries

We extend our approach to the linguistic summarization of (numerical) time series. The main issue boils down to the identification of trends in time series that are characterized by a set of attributes followed by their appropriate aggregation. We propose to use the OWA (ordered weighted averaging) operators for the aggregation of partial trends as an alternative to the use of the classic Zadeh's calculus of linguistically quantified propositions, the Sugeno integral and the Choquet integral. The use of the OWA operators provides a convenient unified aggregation means that can be used to derive diverse types of summaries. The results obtained confirm a high human consistency of linguistic summaries derived.

This paper is a continuation of our previous works on similarity measures of Atanassov intuitionistic fuzzy sets (to be called A-IFSs, for short). The similarity measures we considered used all three functions (membership, non-membership and hesitation) to represent A-IFSs, and examined two kinds of distances - one to an object to be compared, and one to its complement. The disadvantage of those measures is the range of their values - not consistent with the tradition adopted so far for the similarity measures. In this paper we propose a new similarity measure preserving all the advantages of the previously proposed similarity measures and the same time following the commonly assumed number values. We compare the measure proposed with other measure (by Zeng and Li, 2006), and analyze the reasons of the differences (in favour of our measure) in the results.

We show how linguistic data (base) summaries, originated by Yager [26] and further developed first, in a more conventional form, by Kacprzyk and Yager [7], and Kacprzyk, Yager and Zadrozny [8], and then, in a more general context of Zadeh's protoforms, and a more implementation oriented context by Kacprzyk and Zadrozny [16], can be employed for deriving human consistent summaries of Web server logs. Such (short) linguistic summaries make it possible to capture, even by an inexperience and novice user, the essence of what happens as to the accesses to the server. This information may greatly benefit the reporting, advertising, and decision making processes in a company by, e.g., helping improve navigation paths, better organize paid search advertising, personalize Web site access, better designing B2B interfaces, etc.

We propose here some new types of linguistic summaries of time series by extending our previous works. First, the linguistic summaries of time series refer to the summaries of (partial) trends identified here with straight line segments of a piece-wise linear approximation of a time series that is proposed in the paper. To characterize the trends we use the slope of the line segment, the goodness of approximation and the length of the trend. A linguistic summary of a time series is then derived by a linguistic quantifier driven aggregation of trends that is performed using the Sugeno integral. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an eight year period. The results are very promising.

Computing with words (CWW) techniques have been shown to be useful in the management of imperfect information. From the programmer's standpoint, new tools are necessary to ease the use of these techniques within current programming platforms. This paper presents a step in this direction by describing a general framework that supports the implementation of applications dealing with fuzzy objects. We pay special attention to the study of the object comparison problem by offering both a theoretical analysis and a simple and transparent way to use our theoretical results in practice.

Linguistic summaries as descriptions of trends in time series data are proposed. Two general types of such summaries are discussed. The point of departure are linguistic summaries of databases due to Yager. The specificity of time series summarization requires a more general approach to linguistic quantifier based aggregation. Sugeno integrals are employed to address this problem.

Real world decision making is rather complicated -either there are not adequate models or the models are too expensive to derive. The paradigm of case-based reasoning (CBR) of matching new problems to "cases" from a historical database and then adapting successful solutions available from the past to current situations seems to be useful. In this paper we propose to apply intuitionistic fuzzy sets in case-based reasoning. We address in details one but very important problem one inevitably meets when coping with the central tasks of CBR -the calculation of distances (that represent in our paper a similarity) between intuitionistic fuzzy sets. Distances are indispensable, e.g., when concluding about the similarity of cases. We give reasons for using an extended definition of distances for intuitionistic fuzzy sets. It means not only a correct approach from the point of view of fulfilling some mathematical properties but also from the point of view of effective and efficient decision making -i.e., the way making it possible to properly use all the relevant information available. We also discuss incorrect approaches leading to jumping to conclusions.

The purpose of this paper is to propose a new, human consistent way to capture the very essence of a dynamic behavior of some sequences of numerical data. Instead of using traditional, notably statistical type analyses, we propose the use of fuzzy logic based linguistic summaries of data(bases) in the sense of Yager, later developed by Kacprzyk and Yager, and Kacprzyk, Yager and Zadrozny. Our main interest is in the summarization of trends characterized by: dynamics of change, duration and variability. We mainly apply Zadeh's fuzzy logic based calculus of linguistically quantified propositions that may be viewed as an element of his computing with words and perceptions paradigm.

The authors considered first the linguistic data (base) summaries in the sense of Yager, exemplified by, for a personnel database, "most employees are young and well paid" (with some degree of truth) and their extensions. The authors advocate the use of the concept of a protoform (prototypical form), vividly advocated by Zadeh, as a general form of a linguistic data summary. Then, an extension of the interactive approach to fuzzy linguistic summaries was presented, based on fuzzy logic and fuzzy database queries. This paper showed how fuzzy queries are related to linguistic summaries, and that one can introduce a hierarchy of protoforms, or abstract summaries in the sense of latest Zadeh's ideas meant mainly for increasing deduction capabilities of search engines. An implementation for a sales database in a computer retailer, employing some type of a protoform of a linguistic summary was shown

An extension to the classical Boolean model of information retrieval is discussed. The approach is based on recent advances in the area of fuzzy logic in a narrow sense. A strictly formal logical interpretation is provided for all elements of the model including the representation of both documents and queries and the evaluation of queries

Consensus reaching has been widely recognized as an important decision making process. An effective support of this process requires a practical, operational definition of the very concept of consensus. As it is inherently imprecise, it cannot be adequately defined using the classical binary logic. In our previous works, we proposed a definition that is both precise and human consistent. It is based on the Zadeh's calculus of linguistically quantified propositions and may be summarized as follows. There is a consensus when most of the involved individuals agree to a satisfactory degree in respect to most of the important issues. Such a definition provides a continuous assessment of the consensus degree, which makes it an excellent discussion guidance indicator. In the present paper, we extend the array of relevant indicators so as to make the support of consensus reaching, more effective and efficient. We are inspired by the very closely related concept of a linguistic summary of the data. We propose to use the latter for the evaluation of an option's standing, an individual's position and a more elaborate consensus degree.

We apply a new measure of similarity to analyse the extent of agreement in a group of experts. The proposed measure takes into account not only a pure distance between intuitionistic fuzzy preferences but also examines if the compared preferences are more similar or more dissimilar to each other. The agreement of the entire group is assessed via an aggregation of individual testimonies expressed by intuitionistic fuzzy preference relations.

We discuss linguistic summaries of databases introduced by Yager. Starting with our previous work we propose some extensions to the form of a linguistic summary. The new form still fits the scheme of an association rule. However, in comparison to the previous approaches, the use of a range of linguistic values as items and their linguistically quantified aggregation is allowed. An algorithm for mining such association rules within this framework, via the authors' FQUERY for Access package, is presented. Moreover, we show that Zadeh's idea of protoforms, and their hierarchies, can be employed to represent various types of linguistic summaries.

We extend the main idea of a fuzzy analysis of consensus—that is based on a concept of a distance from consensus—to a case when individual testimonies are individual intuitionistic fuzzy preference relations, as opposed to fuzzy preference relations commonly used. Intuitionistic fuzzy preference relations, that in addition to a membership degree (from [0, 1]) include a hesitation margin (concerning the membership degree), can better reflect the very imprecision of testimonies (expressing preferences) of the individuals during the consensus-reaching process. Our new solution, obtained as an interval-valued measure of a distance from consensus, better reflects both real human perception and a soft nature of consensus. © 2003 Wiley Periodicals, Inc.

We propose an improved inductive learning method to derive classification rules that correctly describe most of the examples belonging to a class and do not describe most of the examples not belonging to this class. The problem is represented as a modification of the set covering problems solved by a genetic algorithm. The results are very encouraging.

A general form of a collective choice rule in group decision making under fuzzy preferences and a fuzzy majority is proposed. It encompasses some well known choice rules. Our point of departure is the fuzzy majority-based linguistic aggregation rule (solution concept) proposed by J. Kacprzyk (1985, 1986). This rule is viewed in this paper from a more general perspective, and the fuzzy majority - meant as a fuzzy linguistic quantifier - is dealt with by using R.R. Yager's (1988) ordered weighted averaging (OWA) operators. The particular collective choice rules derived via the general scheme proposed are shown to be applicable in the case of non-fuzzy preferences too.

This paper, is a further development of a combined fuzzy querying and data mining paradigm. The point of departure is the FQUERY for Access. Its earlier version offered the generation of fuzzy association rules within the fuzzy querying interface. We report on extensions to a wider range of available data mining tools, mainly from cluster analysis,and more specifically, a clustering algorithm by Owsinski and Zadrozny. The data to be clustered is first fuzzified using a dictionary of linguistic terms. Additionally, the resulting clusters are helpful in running other data mining tools, notably the generation of association rules.

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.

A combination of flexible querying and data mining is discussed. The framework considered is a classical relational database management querying interface. The flexible querying is here accomplished through a direct use of linguistic, imprecise terms in queries. A popular data mining technique of the association rules is employed to provide for an even more sophisticated querying environment. Some of its extensions are discussed and illustrated. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Originally, most of the popular group decision making rules were conceived for classical (crisp) preference relations (orderings), and then extended to the case of traditional fuzzy preference relations. We propose to further extend them to linguistic preference relations. A Linguistic OWA operators guided aggregation of preferences is employed. The approach proposed is an example of the use of the new paradigm of computing with words/perceptions.

We present an implementation of fuzzy querying over the Internet/WWW. We advance our previous work on the topic, employing the newest developments in Internet technology. While the back-end part of the solution, i.e., the fuzzy querying engine is subject to small changes only, the user interface is completely redesigned. The question of customization of the interface and the number of network roundtrip reduction is the main concern. The possibility of the standardization of the approach is also considered.

We present an implementation (as an add-in to the DBMS) of fuzzy linguistic summaries of sales data of a small-to-medium size computer retailer in Southern Poland. The system derives linguistic summaries exemplified by "about a half of sales of accessories is in autumn" or "about 1/3 of sales of network elements is in the beginning of the year". An inherent imprecision of natural language is accounted for by using elements of fuzzy logic, and to effectively and efficiently search the company's database, a genetic algorithm is employed. The fitting function represents a multiaspect measure of the quality of a linguistic summary. The results obtained turned out to be useful to the owner, and suggested some changes in sales policy, determining the staff size, negotiation of commissions, etc. A combination of fuzzy logic and a genetic algorithm proved to be effective, efficient and synergistic.

We extend the basic Bellman and Zadeh's [Manage. Sci., 17, 141–164 (1970)] model of multistage decision making (control) in a fuzzy environment to include both objective and subjective evaluations of how well fuzzy constraints on decisions (controls) applied and fuzzy goals on states (outputs) attained are satisfied. We discuss the solution by an extended fuzzy dynamic programming model. We present Francelin and Gomide's [Proc. of Second IEEE International Conference on Fuzzy Systems—FUZZ-IEEE'93, San Francisco, CA, Vol. 1, 1993, pp. 655–660] [cf. also Francelin, Gomide, and Kacprzyk [Proc. of Sixth IFSA World Congress, Saõ Paolo, Brazil, Vol. II, 1995, pp. 221–224] and Kacprzyk, Romero, and Gomide [Neuro-Fuzzy Techniques for Information Processing, Physica-Verlag (Springer-Verlag), Heidelberg–New York, forthcoming]] neural network implementing fuzzy dynamic programming, and then show its extension to cover both the objective and subjective evaluations involved in the proposed extension of the basic Bellman and Zadeh's [Manage. Sci., 17, 141–164 (1970)] model. We show its use for solving a socioeconomic regional planning problem proposed in Kacprzyk and Straszak [Applied Systems and Cybernetics, Pergamon, New York, 1982, Vol. 6, pp. 2997–3004; Recent Developments in Fuzzy Sets and Possibility Theory, Pergamon, New York, 1982, pp. 531–541; IEEE Trans. Syst. Man, Cybern., SMC-14, 310–313 (1984)] [cf. Kacprzyk's [Multistage Fuzzy Control, Wiley, Chichester, 1997] book], extending Kacprzyk, Romero, and Gomide [Neuro-Fuzzy Techniques for Information Processing, Physica-Verlag (Springer-Verlag), Heidelberg–New York, forthcoming]. ©1999 John Wiley & Sons, Inc.

We extend the basic Bellman and Zadeh's (1970) model of multistage control (decision making) in a fuzzy environment to include both objective and subjective fuzzy constraints on controls and fuzzy goals on states at the consecutive control stages. Moreover, we consider some aggregation operators to reflect different attitudes towards the satisfaction and substitutability of the fuzzy constraints and fuzzy goals. We present an extended fuzzy dynamic programming model covering those aspects. The extension is motivated by a socio-economic regional planning problem discussed in Kacprzyk and Straszak (1982, 1984), which is outlined in this paper.

We consider the classic Bellman and Zadeh multistage control problem under fuzzy constraints imposed on applied controls and fuzzy goals imposed on attained states with a stochastic system under control that is assumed to be a Markov chain. An optimal sequence of controls is sought that maximizes the probability of attaining the fuzzy goal subject to the fuzzy constraints over a finite, fixed, and specified planning horizon. A genetic algorithm is shown to be a viable alternative to the traditionally employed Bellman and Zadeh dynamic programming. © 1998 John Wiley & Sons, Inc.

We propose a new approach to find a fuzzy set which corresponds to a given intuitionistic fuzzy set (Atanassov, 1986) in a certain sense. This will help extend a huge array of fuzzy properties, models, etc. available to the case of intuitionistic fuzzy sets.

An improved algorithm for inductive learning from erroneous examples is presented. It is assumed that the errors may occur in the attributes' values. However, their location (in which example, and in which attribute) is unknown. Moreover, the errors are assumed incorrigible as it is often the case in practice. A modification of the start-type algorithm is proposed. Importance of the attributes—reflecting, e.g., the attributes' relevance, their proneness to errors, reliability of methods for determining their values, etc.—is elicited from the experts, and weights are determined by Saaty's analytical hierarchy process (AHP). Examples, including an oncological one, illustrating the method proposed are shown. © 1996 John Wiley & Sons, Inc.

Using a fuzzy-logic-based calculus of linguistically quantified propositions, a new database querying system is proposed for handling such imprecise queries as "find all records in which most (almost all, much more than 75 percent, etc.) of the important attributes (out of a specified subset) are as desired (equal to five, greater than ten, around seven, much greater than eleven etc.)."

The determination of regional development policies is discussed. The development proceeds in terms of life-quality indicators: social, economic, environmental, and infrastructural. An evaluation is made with respect to effectiveness and stability. Effectiveness is determined by how well constraints on the consecutive investments are applied and on how well goals relating to the resulting life-quality indicators and the corresponding social satisfactions are fulfilled. Stability is shown by how smoothly the basic development indicators evolve. To deal with an inherent softness, a fuzzy decision model is proposed. An optimal development policy is sought that best satisfies the effectiveness and stability requirements.