In the creation of better multiple attribute decision-making (MADM) patterns to address the ambiguity in the expanding sophisticated of expert systems, the hypothesis of interval-valued intuitionistic fuzzy sets has proven to be an effective and advantageous technique. We employ Aczel–Alsina operations to remedy the MADM issue, wherein all data supplied by decision-makers is conveyed as interval-valued intuitionistic fuzzy (IVIF) decision matrices with all components described by an IVIF number (IVIFN). This allows us to satisfy much more demands from fuzzy decision-making concerns (IVIFN). In the framework of IVIFNs, we primarily describe several novel Aczel–Alsina operations. On the basis of these operations, we construct several novel IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted averaging operator, the IVIF Aczel–Alsina order weighted averaging operator, and IVIF Aczel–Alsina hybrid averaging operator. We built up several features of such operators. We recommend an MADM technique dependent on the advanced IVIF aggregation operators. To demonstrate the effectiveness of the developed technique, we present an overview of research scientist selection. The experimental results show the viability and benefits of the created strategy by contrasting it with the different strategies. This paper reveals that some existing IVIF aggregation operators are particular instances of the operators induced in this paper.

This paper describes the new intuitionistic fuzzy aggregation operators in consequence of Aczel–Alsina operations that possess certain advantages in cases of solving real life problems. We first present some new operations of intuitionistic fuzzy sets (IFSs), for example, Aczel–Alsina sum, Aczel–Alsina product, and Aczel–Alsina scalar multiplication. At that point, we create some IF aggregation operators, for example, the IF Aczel–Alsina weighted averaging operator, the IF Aczel–Alsina ordered weighted averaging operator and IF Aczel–Alsina hybrid averaging operator. We set up different properties of these operators. It is demonstrated that suggested averaging operators have the properties of idempotency, boundary, monotonicity, and commutativity. Then, we design new techniques dependent on these operators to fix multiattribute decision making issues. We present an example of human resource selection to elaborate on the performance of our proposed approach. The outcome shows the practicality and viability of the new technique. Eventually, an organized comparison between the prevailing techniques and the suggested technique has been given.

This study proposes some standard and general forms of induced ordered weighted averaging (GnIOWA) operators where the inductive information is ordered weighted averaging (OWA) weight vectors instead of real numbers. It shows the usefulness of such type of generalized induced OWA in decision-making and evaluation and many other applications. We propose three weights allocation methods that are specifically designed for the proposed GnIOWA operators. For each of the proposed weights allocation methods, a numerical example is also attached accordingly. With the use of convex/concave Regular Increasing Monotone quantifiers, we further discuss some mathematical properties of these weights allocation methods.

The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic linguistic term sets. Further, the generalized Dombi (GD) operators are pretty flexible with the general parameters during the aggregation process. Besides, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between criteria. In this study, we combine the merits of the GD operator, and BM operator for handling multicriteria group decision-making issues under a DPL setting. The existing research on DPL term sets do not focus on both the subjective and objective weights of decision-experts. As a result, the evaluation results are likely to be distorted. To tackle this situation, in this paper, we utilize the concepts of consistency and similarity between the decision-experts to determine the decision-experts subjective and objective weights, respectively. To calculate the weights of criteria, the grey correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. Since the existing aggregation operators fail to capture the interrelations between criteria under DPL setting, so for aggregating criteria values, we propose DPL generalized Dombi BM weighted averaging and geometric aggregation operators. We provide a case study regarding biomass feedstock selection to focus on the applicability of these proposed operators. Furthermore, we investigate the effects of the parameters upon ranking order. We also perform a sensitivity assessment of criteria weights to test the stability of our method. Lastly, we provide a comparison between our approach with various extant methods.

This study first revamps Yager prioritized ordered weighted averaging operators, and condenses them into a conceptual frame with putting aside one realization from Yager's original proposal. Then, based on elicited conceptual frame called Yager prioritized preference conceptual frame, this article proposes three distinct realizations to the conceptual frame with corresponding different instances, in which some evaluation models with weights determination methods are provided. Numerical examples are also presented immediately after every instance. Lastly, this study proposes the concepts of outer monotonic, inner monotonic, and global monotonic weights functions, and discusses some related properties, which are often embodied in preferences of decision makers.

Wiener's highly classified wartime work on prediction used the least squares approach and did not involve probabilities. The approach described in this paper, call it SBPD, for short, is probability-based, but is non-traditional. Moreover, SBPD employs some concepts and techniques drawn from fuzzy logic. Underlying SBPD is what may be called a qualitative Prediction Principle: to a considerable degree the Future replicates the Past and the degree increases when the Future is close to Present and Past. Additionally: in similar circumstances (contexts) similar inputs produce similar outputs. The point of departure in SBPD is a time-series of descriptive variables which take values in a finite set V or finite set W depending on whether the variables are prediction variables or decision variables. X plays the role of History. In SBPD, History is examined and searched for contexts which are similar to the present context. Prediction and conclusion are expressed as probability distributions. SBPD has a potential for applications in many directions which go beyond those which appear in the title of the paper. An algorithm which plays an important role in SBPD involves competition of the degree of similarity of two time-series.

Multiple-criteria decision problems involve selecting an alternative that best satisfies a collection of criteria as quantified by a scalar corresponding to an aggregation of the alternatives satisfaction to the individual criteria. A fundamental issue is the formulation of decision maker's aggregation function based upon the decision maker's perceived relationship between the criteria. Here, we allow the decision maker to express their perceived relationship between the criteria in terms of information about the criteria importances by providing a fuzzy measure over the criteria such that the measure of any subset of criteria is its importance. With the aid of the Choquet integral, we use this fuzzy measure of importances to construct an aggregation function. As the Choquet integral requires an ordering of an alternatives individual criteria satisfactions, special handling is required in the case when criteria satisfactions are interval valued rather then scalar. Here we use the golden rule representative value in the case of interval values.

Existing extensions to Yager's ordered weighted averaging (OWA) operators enlarge the application range and to encompass more principles and properties related to OWA aggregation. However, these extensions do not provide a strict and convenient way to model evaluation scenarios with complex or grouped preferences. Based on earlier studies and recent evolutionary changes in OWA operators, we propose formulation paradigms for induced OWA aggregation and a related weight function with self-contained properties that make it possible to model such complex preference-involved evaluation problems in a systematic way. The new formulations have some recursive forms that provide more ways to apply OWA aggregation and deserve further study from a mathematical perspective. In addition, the new proposal generalizes almost all of the well-known extensions to the original OWA operators. We provide an example showing the representative use of such paradigms in decision-making and evaluation problems.

We introduce the idea of orthopair membership grades and the related idea of general orthopair fuzzy sets. It is noted that these generalize the intuitionistic and Pythagorean fuzzy sets by allowing the support for and against membership to be almost anywhere in [0, 1] × [0, 1], giving systems modelers great freedom in capturing human knowledge. The aggregation of generalized orthopair fuzzy sets is considered with particular concern for the OWA and Choquet aggregation. The concepts of possibility and certainty as well as plausibility and belief are investigated in this general orthopair environment. We study arithmetic operations on general orthopair fuzzy sets. We show how to obtain associated interval valued fuzzy sets from general orthopair fuzzy sets.

The International Journal of Intelligent Systems was created in 1986. Today, the journal is 30 years old. To celebrate this anniversary, this study develops a bibliometric review of all of the papers published in the journal between 1986 and 2015. The results are largely based on the Web of Science Core Collection, which classifies leading bibliographic material by using several indicators including total number of publications and citations, the h-index, cites per paper, and citing articles. The work also uses the VOS viewer software for visualizing the main results through bibliographic coupling and co-citation. The results show a general overview of leading trends that have influenced the journal in terms of highly cited papers, authors, journals, universities and countries.

Linked Open Data (LOD) consists of numerous data stores that are highly interconnected. LOD stores use Resource Description Framework (RDF) as a data representation format. A graph-based nature of RDF brings an opportunity to develop new approaches for accumulating data from multiple sources characterized by different levels of confidence in them. Recently, a participatory learning mechanism has been extended to cope with RDF. It is an attractive way of integrating new pieces of information with already known ones. Further, it has been recognized that pieces of information describing entities can have a disjunctive or conjunctive form. This paper uses an RDF-based participatory learning process to aggregate information obtained from multiple data stores. This process provides mechanisms that determine overall certainty in combined data based on levels of confidence in already known pieces of information and new ones. The behavior of such a process used for integrating information equipped with different levels of uncertainty is presented, and a simple case study is included.

We introduce the Sugeno integral and describe how it can be used to provide a weighted mean-like aggregation of a collection of values drawn from the unit interval. We explain that the underlying measure provides information about the weights associated with the arguments. We provide an alternative view of the Sugeno integral that enables us to extend its use to situations in which the arguments in the aggregation are possibility distributions. We look at the application of the Sugeno integral to the formulation of decision functions in the case of multi-criteria decision making. We focus on the situation where there exists some possibilistic uncertainty in our knowledge of criteria satisfactions by an alternative. We provide operational formulations for the calculation of some notable decision functions in the case of possibilistically uncertain criteria satisfactions.

We introduce Jeffrey's rule of conditioning. We explain how it enables us to determine the current probability of an event using a collection of conditional probabilities of the event determined from past experiences and the current probabilities of the conditioning events. We note the importance of the joint probabilities of the event of interest and the conditioning events in obtaining the required conditional probabilities. We investigate the use of copula's to help obtain these required joint probabilities. We then apply our results to a problem of financial decision making in which the success of the stock issue of a new company depends on the quality of management of company. Here, past history tells information about the success of a typical company based on its quality of management and our own observations provides information about the quality of the current companies management.

Our interest is in the problem of comparing alternatives with uncertain payoffs when the uncertainty is represented using a measure. We first describe various aspects of the use of a measure to represent uncertainty. We recall that probability is a special well-understood example of measure-based uncertainty. We note that stochastic dominance provides a well-established method for comparing alternatives in the case of probabilistic uncertainty. Inspired by this we develop an extension of the use of stochastic dominance for comparing uncertainty profiles to the case where the uncertainty is represented by a measure. We refer to this as measure based stochastic dominance. Do to the fact that in most cases a stochastic dominance relationship does not exist between alternatives this requires us to consider the use of surrogates for measure based stochastic dominance to compare alternatives. Here we investigate a class of surrogates for measure based stochastic dominance that we call Measure Weighted Means (MWM). As we see these MWM are numeric values consistent with measure based stochastic dominance.

The paper addresses a relation between logical reasoning and probability and presents probability-generated aggregators. The obtained aggregators implement probability distributions for specification of generator functions; as it was proven in the paper, such implementation is always possible. In the paper, the relation between neutral element of the probabilistic uninorm and parameters of the underlying probability distribution is demonstrated, and a method for specification of the probabilistic uninorm, and thus—of the probability distribution using t-norm and t-conorm—is constructed. In addition, the obtained probabilistic uninorm and probabilistic absorbing norm or nullnorm are briefly considered as algebraic operations on the open unit interval. In is demonstrated, that, in general, the obtained algebra is nondistributive and depends on the distributions, which are used for generating probabilistic uninorm and absorbing norm. The obtained results bridge several gaps between fuzzy and probabilistic logics and provide a basis both for theoretical studies in the field and for practical techniques of digital/analog schemes synthesis and analysis.

We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π-i numbers. We investigate operations that are closed under Π-i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π-i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.

Our focus is on decision making in uncertain environments. We first introduce the Dempster–Shafer framework to model the uncertainty associated with possible outcomes. We then describe an approach for decision making when our uncertainty is captured using the Dempster–Shafer model and where the payoffs are numeric values. An important part of this approach is the role of the decision attitude as well as the aggregation of the possible payoffs. We then look at the situation where the payoffs, rather than being numbers, are values drawn from an ordinal scale. This requires us to provide appropriate operations for combining payoffs drawn from an ordinal scale.

We first recall the concept of Z-numbers introduced by Zadeh. These objects consist of an ordered pair (A, B) of fuzzy numbers. We then use these Z-numbers to provide information about an uncertain variable V in the form of a Z-valuation, which expresses the knowledge that the probability that V is A is equal to B. We show that these Z-valuations essentially induce a possibility distribution over probability distributions associated with V. We provide a simple illustration of a Z-valuation. We show how we can use this representation to make decisions and answer questions. We show how to manipulate and combine multiple Z-valuations. We show the relationship between Z-numbers and linguistic summaries. Finally, we provide for a representation of Z-valuations in terms of Dempster–Shafer belief structures, which makes use of type-2 fuzzy sets. © 2012 Wiley Periodicals, Inc.

Our focus is on the representation of uncertain information using set measures. We first discuss the basic properties of monotonic set measures. We then discuss the appropriateness of their use in modeling uncertain information. We look at some notable types of measures of uncertain information and investigate in considerable detail cardinality-based measures. We look at the Sugeno measure and provide a formulation of the underlying cardinality-based measures. We then look at quasi-additive uncertainty measures. We discuss the entropy and attitudinal character of an uncertainty measure. Finally, we introduce the ideas of the assurance and opportunity of the occurrence of an outcome. © 2012 Wiley Periodicals, Inc.

We introduce a measure of diversity related to the problem of selecting n objects from a pool of candidates lying in q categories. We introduce the concept of target diversity index (TDI) and describe various agendas for defining it. We look at the problem of trying to select elements to satisfy some desirable criterion that additionally satisfies a requirement of being diverse. We suggest some aggregation methods for combining these multiple criteria. © 2010 Wiley Periodicals, Inc.

The recent development of Web 2.0 has provided an enormous increase in human interactions across all corners of the earth. One manifestation of this is the growth of computer mediated social networks. Many notable Web 2.0 applications such as Facebook, Myspace and LinkedIn are social networks. Relational networks are becoming an important technology for modeling these types of social networks and the type of collaborative intelligence that arises from these interactions. Our goal here is to enrich the domain of social network modeling by introducing ideas from fuzzy sets and related granular computing technologies to provide a bridge between a human network analyst's linguistic description of social network concepts and the formal model of the network.

Our focus here is to provide a methodology that can be used by a participant in an adversarial decision-making environment to help choose their action. Central to our approach is the use of knowledge and perceptions about one's adversary to obtain an uncertainty profile indicating which action the adversary will take. Once having this uncertainty profile, the problem of deciding which action to take becomes a problem of decision making under uncertainty. Here, we make considerable use of the Dempster--Shafer belief structure as a way of formalizing the uncertainties. © 2008 Wiley Periodicals, Inc.

An introduction to some basic ideas of graph (relational network) theory is first provided. We then discuss some concepts from granular computing in particular the fuzzy set paradigm of computing with words. The natural connection between graph theory and granular computing, particularly fuzzy set theory, is pointed out. This connection is grounded in the fact that these are both set-based technologies. Our objective here is to take a step toward the development of intelligent social network analysis using granular computing. In particular one can start by expressing in a human-focused manner concepts associated with social networks then formalize these concepts using fuzzy sets and then evaluate these concepts with respect to social networks that have been represented using set-based relational network theory. We capture this approach in what we call the paradigm for intelligent social network analysis, PISNA. Using this paradigm, we provide definitions of a number of concepts related to social networks. © 2008 Wiley Periodicals, Inc.

The Internet holds huge amount of documents available for users. Effective utilization of this enormous repository means a need for systems supporting users in a process of finding related documents. An ontology defined in the framework of the Semantic Web (Berners, 2001) allows for specification of concepts, their instances, and relationships existing between concepts. A hierarchy of concepts (Yager, 2000) is a graph-like structure providing a means for representing human-like dependencies. The article proposes an approach for utilization of a hierarchy of concepts to perform categorization of web pages in the Semantic Web. A user provides a hierarchy that can only partially “cover” their domain of interest. The hierarchy is treated as a “seed” representing user’s initial knowledge about the domain. Ontologies are treated as supplementary knowledge bases. They are used to instantiate the hierarchy with concrete information, as well as to enhance it with new concepts initially unknown to a user.

Fuzzy cognitive maps (FCMs) allow experts to express their knowledge by drawing weighted causal digraphs. Experts can pool or fuse their knowledge by adding the underlying FCM causal matrices. This naturally extends the ordered-weighted-averaging (OWA) technique to averaging dynamical systems and can create complex dynamical systems from several simpler ones. Edge quantization allows experts to state their knowledge in the simpler terms of causal increase (1), decrease (−1), or absence (0). We model the expert FCMs as a sequence of random fields to study the small-sample effects of quantizing both the causal edges and the fuzzy-set concept nodes. The averaged quantized random matrices exhibit large-sample convergence to the population means of the unquantized matrices in accordance with the Strong Law of Large Numbers. But the small-sample averages can show substantial diversity of equilibrium attractors (fixed points or limit cycles). We use statistical tests—chi-square tests, Spearman's rank coefficient, the Kolmogorov–Smirnov test, and the fuzzy equality of limit cycle histograms—to show that this small-sample equilibrium diversity increases as the node multivalence or fuzzy-set quantization increases. The appendix presents a new probabilistic convergence theorem that shows that edge quantization or thresholding does not affect FCM combination for large expert sample sizes: the sample mean of quantized expert causal edge values converges with probability one to the population mean causal edge values. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 181–202, 2007.

Future automated question answering systems will typically involve the use of local knowledge available on the users' systems as well as knowledge retrieved from the Web. The determination of what information we should seek out on the Web must be directed by its potential value or relevance to our objective in the light of what knowledge is already available. Here we begin to provide a formal quantification of the concept of relevance and related ideas for systems that use fuzzy-set-based representations to provide the underlying semantics. We also introduce the idea of ease of extraction to quantify the ability of extracting relevant information from complex relationships. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 385–396, 2007.

Considerable concern has arisen regarding the quality of intelligence analysis. This has been, in large part, motivated by the task of determining whether Iraq had weapons of mass destruction. One problem that made this analysis difficult was the uncertainty in much of the information available to the intelligence analysts. In this work, we introduce some tools that can be of use to intelligence analysts for representing and processing uncertain information. We make considerable use of technologies based on fuzzy sets and related disciplines such as approximate reasoning. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 523–544, 2006.

Abstract We point out that question‐answering systems differ from other information‐seeking applications, such as search engines, by having a deduction capability, an ability to answer questions by a synthesis of information residing in different parts of its knowledge base. This capability requires appropriate representation of various types of human knowledge, rules for locally manipulating this knowledge, and a framework for providing a global plan for appropriately mobilizing the information in the knowledge to address the question posed. In this article we suggest tools to provide these capabilities. We describe how the fuzzy set–based theory of approximate reasoning can aid in the process of representing knowledge. We discuss how protoforms can be used to aid in deduction and local manipulation of knowledge. The idea of a knowledge tree is introduced to provide a global framework for mobilizing the knowledge base in response to a query. We look at some types of commonsense and default knowledge. This requires us to address the complexity of the nonmonotonicity that these types of knowledge often display. We also briefly discuss the role that Dempster‐Shafer structures can play in representing knowledge.

We consider the problem of multicriteria decision making. We indicate how the evaluation of an alternative involves a determination of the degree to which subsets of criteria are satisfied by the alternative. This calculation is based upon an anding of the satisfactions of the individual criteria in the subsets. We consider the possibility of using t-norms other than the Min for the and operation. Using this generalization we develop an extension of the OWA operators, called the TOWA, which involves a mixing of the t-norm with the OWA operator. We extend this generalization to other aggregation techniques, the Choquet and Sugeno integrals. We introduce the concept of the Power of a t-norm to provide an ordering over the t-norm operators. We look at Power of a number of families of t-norm. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 453–474, 2005.

We introduce the t-norm and discuss the representation of this operator by additive generators. An approach is suggested for including importances in t-norm aggregation taking advantage of this representation of the t-norm. We look at formulations resulting for a variety of t-norms. We then apply the approach to the t-conorm and look at its effect on a variety of t-conorms. Finally, we turn to the uninorm and suggest an analogous method for including weighting in uninorm aggregations. © 2004 Wiley Periodicals, Inc.

We focus on the problem of decision-making in the face of uncertainty. The issue of the representation of uncertain information is considered and a number of different frameworks are described: possibilistic, probabilistic, belief structures, and graded possibilistic. We suggest methodologies for decision-making in these different environments. The importance of decision attitude in the construction of decision functions is strongly emphasized. © 2002 Wiley Periodicals, Inc.

We discuss the fuzzy integral. The centrality of the ordering operation, based upon the arguments to be aggregated, is pointed out. We then extend the fuzzy integral aggregation operator by allowing the ordering operation to be based upon values other then those being aggregated. This leads to the induced fuzzy integral aggregation operator. We look at this new operator and study its properties. We show its relationship to a formulation called limited fuzzy integral aggregation. It is shown how this new induced fuzzy integral operator provides a natural framework for the implementation of nearest neighbor rules. Throughout this work, use is made only of the ordinal aspects of the information used. © 2002 Wiley Periodicals, Inc.

Dempster–Shafer belief structures provide a useful framework for the representation of information about a variable whose value is uncertain. Important parameters in these structures are the weights associated with the focal elements. These weights, which can be viewed as probabilities, are required to be precisely known. Here we relax this requirement and we consider the situation in which our knowledge of the weights associated with the focal elements is that they lie in some known interval rather then being precisely specified. This relaxation will allow us to more realistically model situations in which the weights cannot be precisely obtained. At a formal level, this situation can be viewed as one in which we have some uncertainty as to what is the actual belief structure, this uncertainty being of the possibilistic type. We introduce the measures of plausibility and belief in this environment. We also look at the issue of combining belief structures for these interval type belief structures. © 2001 John Wiley & Sons, Inc.

In this paper, we focus on the web-shopping activity and on ways to improve the quality of the information available to consumers. We describe a tool, called a product space map, for the presentation of information about a product category which can help consumers in making purchasing decisions. Using this tool we first provide a clustering or segmentation of a product line, that is, 27-inch televisions, into price categories such as low end, moderate and high end. Once having this partitioning we then use the idea of linguistic summaries to describe the properties of each category with respect to relevant features. An example of such a summary is “Most TV's in the high price category provide extremely high resolution.” With the aid of such information it becomes much easier for consumers to understand the product line, see what they are getting for their money, and more easily and confidently locate products that are of particular value for the money. Considerable use is made of fuzzy set technology to provide the ability to describe the information in a way, using linguistic expressions, that is particularly consumer friendly. © 2001 John Wiley & Sons, Inc.

We consider the problem of information fusion, specifically the task of fusing information from two different categories, information which is directly about an object of interest (OBJOIN information) and information about related objects (peer information). We discuss the representation of these different types of information, the first in terms of a possibilistic distribution and the second in terms of a probability distribution. We introduce an approach to information fusion based upon the use of the fuzzy modeling technology. In this approach we represent the fusion function in terms of rules which indicate when to use the different types of information. Particularly notable here is the role of information quality as a guiding factor in the fusion process. © 2001 John Wiley & Sons, Inc.

We provide an overview of the theory of approximate reasoning and discuss the measurement of information in this reasoning system using specificity. It is then shown how to represent the binary propositional logic in the framework of approximate reasoning. Using the measure of specificity we show how to measure the information contained in the propositions of binary logic. Our measure essentially measures the proportion of possibilities eliminated by the proposition. Next we turn to the possibilistic logic and show how to represent this within the framework of approximate reasoning. We again, using specificity, provide for a measure of information of propositions in this logic. Finally we turn to the issue of quantified statements and show how to represent general quantified statements involving predicates within these two logics. ©1999 John Wiley & Sons, Inc.

Here the Dempster–Shafer belief structure is viewed as providing partial information about the underlying fuzzy measure associated with a uncertain variable. In this perspective there exists many possible fuzzy measures that can be associated with a Dempster–Shafer belief structure. Typically only two of these measures have been made explicit, those being the measure of belief and plausibility. Here we introduce a whole class of fuzzy measures that can be associated with a Dempster–Shafer belief structure. As an aid to choosing between these myriad of possibilities we discuss the entropy of a fuzzy measure. ©1999 John Wiley & Sons, Inc.

The importance as well as the difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. Specifically we focus on expected value type valuations which are based upon the transformation of a fuzzy subset into an associated probability distribution. We develop a number of families of parameterized valuation functions. ©1999 John Wiley & Sons, Inc.

In this work, we focus on the OWA operator. We view this operator as the inner product of two vectors: a weighting vector containing the weights associated with the aggregation, and a second vector containing the arguments to be aggregated. We note the centrality to this operator of the process used to index the elements in the argument vector, and suggest some new mechanisms for ordering the arguments. In the second part, we study the situation in which the weighting vector is context dependent. Finally, we consider the case in which the arguments to be aggregated are drawn from an ordinal scale; the solution to this problem leads us to consider random weighting vectors. © 1998 John Wiley & Sons, Inc.

We investigate the problem of fusing collections of documents provided by multiple information retrieval systems. A parameterized approach is suggested in which a parameter determines how the documents in the individual collections are interleaved to form a fused list of documents. We then suggest a mechanism for learning this parameter.

We consider the problem of fusion of multiple information sources, particularly in environments when the sensor observations are imprecise. The concept of a combinability relationship is introduced to enable the inclusion in the fusion process of information about the appropriateness of fusing different elements from the observation space. This idea allows for the use of an expert knowledge base, containing information about the domain of the particular problem, in the fusion process and leads to a more intelligent aggregation. We show that if we use a combinability relationship that only allows fusion of identical elements then the only idempotent fusion of any collection of fuzzy observations is their intersection. Using the idea of the fuzzy measure we considered situations in which we allow a partial collection of the observations determine the fused value. © 1997 John Wiley & Sons, Inc.

The concept of typicality is studied and the relationship between a typical value and the mode is explored. It is suggested that a typical value should be a fuzzy subset. A measure of typicality associated with any fuzzy subset is introduced. We provide an algorithm for finding the best typical value which is of the form of an interval. © 1997 John Wiley & Sons, Inc.

We describe a new paradigm for the inclusion of advertisements on the WWW. This paradigm takes advantage of the internet's great ability for instantaneous online processing of information in real time. A methodology is described for the use of intelligent agents to help in the determination of the appropriateness of displaying a given advertisement to a visitor to a site using very specific information about potential customers. Use is made of fuzzy systems modeling for the construction of these agents. © 1997 John Wiley & Sons, Inc.

We consider multicriteria aggregation problems where, rather than requiring all the criteria be satisfied, we need only satisfy some portion of the criteria. The proportion of the critera required is specified in terms of a linguistic quantifier such as most. We use a fuzzy set representation of these linguistic quantifiers to obtain decision functions in the form of OWA aggregations. A methodology is suggested for including importances associated with the individual criteria. A procedure for determining the measure of “orness” directly from the quantifier is suggested. We introduce an extension of the OWA operators which involves the use of triangular norms. © 1996 John Wiley & Sons, Inc.

In this work we consider a fuzzy set based approach to the issue of discovery in databases (database mining). The concept of linguistic summaries is described and shown to be a user friendly way to present information contained in a database. We discuss methods for measuring the amount of information provided by a linguistic summary. The issue of conjecturing, how to decide on which summaries may be informative, is discussed. We suggest two approaches to help us focus on relevant summaries. The first method, called the template method, makes use of linguistic concepts related to the domain of the attributes involved in the summaries. The second approach uses the mountain clustering method to help focus our summaries. © 1996 John Wiley & Sons, Inc.

The focus of this article is on the issue of information aggregation. We introduce two new aggregation operators, called MOM and MAM operators, which are, respectively, generalized and and or operators. We describe their relationship to the multivalued logic triangular norm operators and show how they generalize these operators by weakening the associativity property. We provide a duality theorem between these new operators. We present some special classes of these operators. We extend these operators to allow for weighted aggregations, which enable us to include importances. We introduce some families of these weighted MOM and MAM operators. We show how the typical neural aggregation is a special class of these weighted MOM and MAM operators. This generalization allows us to consider neural network and fuzzy logic methods in the same framework. © 1995 John Wiley & Sons, Inc.

We consider a general characterization of a measure of ambiguity suggested by Fishburn and investigate the appropriateness of this characterization. It is shown that a number of concepts related to uncertainty and taken from fuzzy logic-measures of fuzziness, measures of specificity, and measures of possibility/certainty interval-satisfy this characterization. In addition, a measure from classical logic indicating the certainty of our knowledge of the truth or falsity of a proposition in the face of a collection of premises also satisfies the characterization of Fishburn. © 1995 John Wiley & Sons, Inc.

The problem of decision making under doubt is described. the concept of immediate probabilities is introduced. It is seen as a modification of typical probabilistic knowledge with information about the payoffs, mediated through dispositional information (optimism/pessimism), resulting in a modified formulation of an agents perception of the probabilities in effect in the current decision. We use the Dempster rule of combination to help obtain an expression for these probabilities. We show how immediate probabilities allows us to explain the Allais paradox. A number of properties of these probabilities are described. the strategic use of these probabilities are explored as a means for effecting other people's decisions. © 1995 John Wiley & Sons, Inc.

We discuss the idea of a linguistic quantifier and fuzzy set representations of these objects. We describe two formalisms for evaluating the truth of linguistically quantified propositions such as Most winter days are cold. the first approach is based upon a probabilistic interpretation and the second is based upon a logical interpretation, and uses a generalization of the “and” and “or” operations via OWA operators. We suggest an application of these quantified statements for the representation of the quotient operator in fuzzy relational data bases. © 1994 John Wiley & Sons, Inc.

We discuss the participatory learning model originally introduced by Yager [IEEE Trans. Syst. Man Cybern. SMC-20, 1229–1234 (1990)]. We analyze the learning mechanism as a stable control strategy. We show how the learning mechanism used in participatory learning can be expressed in the form of a fuzzy rule base. We use this rule base formulation to provide new learning rules. We modify the Widrow-Hoff rule to include a participatory learning mechanism. © 1993 John Wiley & Sons, Inc.

We apply the fuzzy description to some analytic models of combat, based on ordinary differential equations. the extension to a more involved partial differential equations model is briefly mentioned. the merits of the fuzzy description versus the deterministic or probabilistic descriptions are discussed.

We describe the aggregation process of the typical artificial neuron. We introduce the concept of a fuzzy linguistic quantifier and describe the process for determining the truth of propositions containing linguistic quantifiers. We show how this truth value can be viewed as the firing level of an artificial neuron. We show the relationship between fuzzy sets and neural inputs. A new class of neurons called owa-neurons is described. A learning algorithm for this class of neurons is presented. We provide a methodology for processing information in non-numeric neural networks. © 1992 John Wiley & Sons, Inc.

Defuzzification in fuzzy logic controllers concerns itself with the issue of selecting an appropriate crisp value from the fuzzy output of the controller. We provide a parametized family of defuzzification operations. We call this family BAsic Defuzzification Distributions (BADD). We show that the commonly used methods. Mean of Maximum and Center of Area are special cases of this family. We suggest the use of these BADD transformations form the basis of a learning scheme to obtain the optimal defuzzification method in a given application. We suggest that the parameter in the BADD family, the distinction between different defuzzification methods, is related to the confidence we have in the rest of the controller.

A formal deductive view for the theory of approximate reasoning, called AR-1, is introduced. A central feature of this framework is the view of propositions as statements involving the assignment of possible values to variables. A unified method for managing joint variables is given. AR-2, which allows for the introduction of probability theory into approximate reasoning, is presented. AR-5, a restrictive version of approximate reasoning, is also introduced.>

We described teh theories of approximate reasoning and mathematical evidence. We show that in the face of possibilistic uncertainty they lead to equivalent inferences. After approapriateely extending the mathematical theory of evidence to the fuzzy environment we show that these two theories are equievalent in the face of fuzzy and possiblistic uncertainty.

We discuss the rule of inference called the entailment principle which plays a significant role in the possibilistic type reasoning used in the theory of approximate reasoning. We extend this principle to situations in which the knowledge is a type of combination of possibilistic and probabilistic information which we call Dempster—Shafer granules. We discuss the conjunction of these D—S granules and show that Dempster's rule of combination is a special application of conjunction followed by a particular implementation of the entailment principle.