Artificial neural networks are a dominant force in our modern era of data-driven artificial intelligence. The adaptive neuro fuzzy inference system (ANFIS) is a neural network based on fuzzy logic versus a more traditional premise like convolution. Advantages of ANFIS include the ability to encode and potentially understand machine learned neural information in the pursuit of explainable, interpretable, and ultimately trustworthy artificial intelligence. However, real-world data is almost always imperfect, e.g., incomplete or noisy, and ANFIS is not naturally robust. Specifically, ANFIS is susceptible to over inflated uncertainty, poor antecedent (fuzzy set) data alignment, degenerate optimization conditions, and hard to interpret logic, to name a few factors. Herein, we explore the use of possibilistic clustering to identify outliers, specifically typicality degrees, to increase the robustness of ANFIS; or any fuzzy logic neuron/network. Experiments are presented that demonstrate the need and quality of the proposed solutions in the pursuit of robust interpretable machine learned neuro fuzzy logic solutions.

The Choquet integral (ChI) is a proven tool for information aggregation. In prior work, we showed that learning a ChI from data results in missing variables. Herein, we explore two ways to transfer a known ChI from a source domain to a new under sampled target domain. The first method is based on regularization and it listens to the full source domain ChI. The second method optimizes what we can observe (target domain supported variables) and missing variables are the only thing migrated from the source domain. Synthetic experiments, aka we know the truth, are used to show the behavior of these methods with respect to transfering between ChIs.

In numerous applications, spatiotemporal graphs are studied to exploit the structure of underlying data to characterize, control, or predict behavior. Nodes of these graphs exhibit spatiality, while edge connectivity and weighting may be derived from spatial conditions of the incident nodes. Because of the complexity added by the temporal dimension, these graphs are typically modeled in part as a stochastic processes. Though numerous application-defined spatiotemporal graphs with stochastic parameterizations exist, a general stochastic process for such graphs has not yet been formally defined in the literature. In an effort to move towards generalization, we offer a brief introduction to the Stochastic SpatioTemporal (SST) graph model, which describes a graph as a set of initially observed nodes and several sets of stochastic processes: one describing node motion, one describing edge connectivity, and one describing edge weight variation. We propose a Monte Carlo method framework by which temporal graph algorithms that yield numerical or set-based results may be studied for conditions of stability. We demonstrate such a framework by way of a geometric SST graph, which is defined based on the geometric random graph exhibiting Brownian motion of nodes. We offer results to show the points at which node movement and edge weight variation cause the geometric SST graph to become unstable for predicting least-cost paths. Finally, we discuss ongoing research projects and plans currently being undertaken to study and utilize stochastic properties of spatiotemporal network data.

Information fusion is an essential part of nearly all systems whose goal is to derive decisions from multiple sources. Often, a fusion solution has parameters and the goal is to learn them from data. Herein, we propose efficient evolutionary algorithm (EA) operators to facilitate learning the Choquet integral (ChI). Whereas many EAs provide a way to solve complex, unconstrained optimization tasks, most tend to perform relatively poor in light of constraints. Recently, a few EA-based approaches to optimizing the ChI have appeared. Namely, these methods focus on fixing the values of variables so conditions are met or feasible candidate pairs are identified for steps such as crossover. Herein, we introduce a new set of transparent operators that are guaranteed to naturally preserve constraints, thus eliminating the need to resort to costly evaluations and fixing of constraint violations. In particular, our method scales well to large numbers of inequality constraints, something that prior work does not. The proposed algorithm, coined efficient ChI genetic algorithm (ECGA), is evaluated on several synthetic data sets and it is compared with state-of-the-art algorithms. In particular, we show benefits in terms of solutions found and the time it takes to find such an answer.

Numerous applications in engineering are plagued by incomplete data. The subject explored in this article is how to extend the fuzzy integral (FI), a parametric nonlinear aggregation function, to missing data. We show there is no universally correct solution. Depending on context, different types of uncertainty are present and assumptions are applicable. Two major approaches exist, use just observed data or model/impute missing data. Three extensions are put forth with respect to just use observed data and a two step process, modeling/imputation and FI extension, is proposed for using missing data. In addition, an algorithm is proposed for learning the FI relative to missing data. The impact of using and not using modeled/imputed data relative to different aggregation operators-selections of underlying fuzzy measure (capacity)-are also discussed. Last, a case study and data-driven learning experiment are provided to demonstrate the behavior and range of the proposed concepts.

Uncertainty in spatial geometrical issues is represented using Dempster-Shafer (D-S) theory. Interval approaches are used for D-S uncertainty of spatial locations and the associated arithmetic operations on such intervals described. Categories of uncertainty for points and lines are defined using interval formulations. Based on these, approaches for calculation of geometric areas, line length and line slopes are given. Compatibility of imprecise point locations is discussed and potential aggregations for similar points considered. Finally, topological spatial relationships are described for objects with uncertain boundaries. This will provide a formal framework for the use of a D-S interval approach for uncertainty in spatial geometric issues.

Evidence resolution has been studied previously for crisp hierarchies and here we develop approaches for fuzzy concept hierarchies. Since fuzzy hierarchies are characterized by decompositions of their domains as opposed to partitions, properties and measures of decompositions are developed. Fuzzy complete and partial evidence resolution is defined and related to the valuation of evidence. Finally a for-and-against analysis is developed for the selection of which concept to choose in the generalization.

An approach is developed for object similarity to support a focus on the role of extreme values in object matching, which is termed hypermatching. Importance weights are first introduced to the matching and variations formulated for objects that do not share all the same attributes. Extreme attribute values are considered by introducing amplification of attribute importance and several significant cases examined. The objects can both possess the same or different extreme valued attributes. Another case is where one object may have an extreme attribute, which the other object does not have. Then, the analysis of the effect of multiple extreme attributes is presented. Finally for attributes with 0-1 values (features), similarity matching is considered and a closed form solution for the similarity is developed. This provides the basis for the Yager-Petry index, which is then compared with the Jaccard similarity index.

In this paper, we present a number of approaches using fuzzy set theory to influence decision-making behavior, which is a type of human persuasion. We couch the approach as the process to draw a conclusion “V is P” given “V is F,” where P is a fuzzy subset of F representing some linguistic value for V that corresponds to a perception of the world V is P, which we want a person to accept. We examine several methods to represent the process to engender such influences. These include using a person's predispositions, framing the context of a discussion and generalization techniques that allow issues to be viewed in a more favorable light. Finally, we discuss approaches to the related topic of negotiations. This paper describes these approaches and the required background formalisms that are used in them.

In this paper, we develop characterizations of the properties of categories. We introduce an approach to representing imprecise hierarchies based on the idea of fragmentation. In the case of fuzzy categories, measures of how well fuzzy categorization satisfies the concept of a partitioning for such categories are developed. Finally, issues that are involved in the formulation of fuzzy categorization of a domain using approaches based on the use of prototypes are considered.

This paper describes a conceptual and theoretical framework for the resolution of seemingly contradictory evidence for decision-making. Basic to this approach is the use of granulation provided by the categories obtained by ascending concept hierarchies. This process will be driven by the use of a criterion that represents the utility of granular categories to the user's decision making. The definition of complete and partial evidence resolution and their properties are developed, which permits the formulation of the concept of preponderance of evidence for the decision maker. Finally, we show some preliminary results on the concepts of strength and consensus measures to provide metrics of the goodness of the evidence resolution.

In this article we investigate an attribute-oriented induction approach for acquisition of abstract knowledge from data stored in a fuzzy database environment. We utilize a proximity-based fuzzy database schema as the medium carrying the original information, where lack of precise information about an entity can be reflected via multiple attribute values, and the classical equivalence relation is replaced with the broader fuzzy proximity relation. We analyze in detail the process of attribute-oriented induction by concept hierarchies, utilizing the original properties of fuzzy databases to support this established data mining technique. In our approach we take full advantage of the implicit knowledge about the similarity of original attribute values, included by default in the investigated fuzzy database schemas. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 763–779, 2007.

Access and retrieval of meteorological and oceanographic data from heterogeneous sources in a distributed system presents many issues. There are a number of features of the TEDServices system that illustrate active network management for such data. There is a self-aware or intelligent aspect with respect to the mechanisms for shutdown, data ordering, and propagation of data orders. Intelligent cache management and collaborative application sharing process are other features of the active network management. Additionally a very important capability is the implementation of resumable object streams, which allows either the client or server side of a request to lose network connection, regain it, and the request will continue where it left off. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1123–1138, 2007.

This paper describes a conceptual and theoretical framework to allow better user control over data summarization for knowledge discovery. Basic to the approach is a measure of quality of summarization of data using categories provided by the hierarchical structure of concept ontology. This involves the modeling, using a fuzzy sets approach, of the four criteria implicit in a summarization imperative: minimum coverage, minimum relevance, succinctness, and usefulness. With these criteria modeled, a multicriteria approach is presented, using a decision function aggregating these criteria that provides an overall quality measure to guide the summarization of the data. The development of the theory is first presented for the simple case of a single attribute to clearly delineate the basic issues and approach and then extended to multiple attributes. Finally, approaches to provide a more user-oriented presentation of the summarized data are considered

In this paper we investigate application of fuzzy concept hierarchies to mining multi-level knowledge from large datasets via a well-known attribute-oriented induction approach (Han and Kamber, 2000). We analyze in detail the original process of fuzzy hierarchical induction and extend it with two new characteristics which improve applicability of the original approach to scientific data mining. These are a consistency of our fuzzy induction model, and an approximate drilling-down technique allowing a user to retrieve estimated explanations of the generated abstract concept. An application to discovery of multi-level association rules from environmental data stored in a toxic release inventory is presented

Uncertainty management is necessary for real world applications, especially those used with data mining. The Region Connection Calculus (RCC) and egg-yolk methods have proven useful for the representation of vague regions in spatial data. Rough set theory has been shown to be an effective tool for data mining and for uncertainty management in databases. In this study we use a rough set foundation for expressing topological relationships previously defined for the RCC and egg-yolk methods and show that rough sets can improve on the representation of topological relationships and concepts defined with the other models, which leads to improved mining of spatial data. Finally, we provide an extension of spatial association rule generation that will be able to use rough set–modeled spatial data. © 2004 Wiley Periodicals, Inc.

For many years, spatial querying has been of interest for the researchers in the GIS community. Any successful implementation and long-term viability of the GIS technology depends on the issue of accuracy of spatial queries. In order to improve the accuracy and quality of spatial querying, the problems associated with the areas of fuzziness and uncertainty need to be addressed. There has been a strong demand to provide approaches that deal with inaccuracy and uncertainty in GIS. In this paper, we develop an approach that can perform fuzzy spatial querying under uncertainty. An inexact inferencing strategy for objects with determined and indeterminate boundaries is investigates using type-2 fuzzy set theory.

The RCC and egg-yolk methods have proven useful for representation of vague regions in spatial data. Here we model them using rough set theory. This then develops the basis to allow a rough set approach to uncertainty in spatial relationships for association rules and other forms of spatial data mining.

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.

This paper concerns the modeling of imprecision, vagueness, and uncertainty in databases through an extension of the relational model of data: the fuzzy rough relational database, an approach which uses both fuzzy set and rough set theories for knowledge representation of imprecise data in a relational database model. The fuzzy rough relational database is formally defined, along with a fuzzy rough relational algebra for querying. Comparisons of theoretical properties of operators in this model with those in the standard relational model are discussed. An example application is used to illustrate other aspects of this model, including a fuzzy entity–relationship type diagram for database design, a fuzzy rough data definition language, and an SQL-like query language supportive of the fuzzy rough relational database model. This example also illustrates the ease of use of the fuzzy rough relational database, which often produces results that are better than those of conventional databases since it more accurately models the uncertainty of real-world enterprises than do conventional databases through the use of indiscernibility and fuzzy membership values. ©2000 John Wiley & Sons, Inc.

Use of a genetic algorithm assumes the existence of a figure of merit called fitness, for which there is a value for every candidate solution. The fitness must be measurable over the representation of the solution by means of a computable function. The fitness function is, in most cases, independent of the other factors, including the algorithm used. Often, the fitness is an estimation of the nearness to an ideal solution or the distance from a default solution. In image scene interpretation, the solution takes the form of a set of labels corresponding to the components of an image and its fitness is difficult to conceptualize in terms of distance from a default or nearness to an ideal. Here we describe a model in which a semantic net is used to capture the salient properties of an ideal labeling. Instantiating the nodes of the semantic net with the labels from a candidate solution (a chromosome) provides a basis for estimating a logical distance from a norm. This domain-independent model can be applied to a broad range of scene-based image analysis tasks. © 2000 John Wiley & Sons, Inc.

Trends in databases leading to complex objects present opportunities for representing imprecision and uncertainty that were difficult to integrate cohesively in simpler database models. In fact, one can begin at the conceptual level with a model that allows uncertainty assumptions and then transform those assumptions into a logical model having the necessary semantic foundations upon which to base a meaningful query language. Here we provide such a constructive approach beginning with the ExIFO model for expression of the conceptual design then show how the conceptual design is transformed into the logical design (for which we utilize the extended NF/sup 2/ logical database model). The steps are straightforward, unambiguous, and preserve the relevant information, including information concerning uncertainty.

In this article, we present a model for defining and representing binary topological and directional relationships between 2-dimensional objects that is used to provide a basis for fuzzy querying capabilities. The definition of the relationships is based on an extension of Allen's temporal relations (Allen, 1983) to the spatial domain. This is done by allowing each of Allen's 13 relations to represent the interaction of 2-dimensional objects in terms of an x and y relationship component. The resulting set of relationships is then used for defining topological and directional relationship terminology. A data structure called an abstract spatial graph (ASG) is defined for the binary relationships that maintains all necessary information regarding topology and direction. Abstract spatial graphs provide the basis for processing of fuzzy topological and directional queries. © 1998 John Wiley & Sons, Inc.

There have been significant theoretical advances in fuzzy database technology, yet commercially its successes have been negligible. This article examines the current state of this technology and suggests directions for future efforts. A framework for the analysis of fuzzy database technology is proposed and extant models are examined with reference to this framework. Fuzzy databases are studied in relation to the requirements of the database community. It is argued that new generation applications and object-oriented databases hold the key to the future commercial acceptability of this technology. © 1996 John Wiley & Sons, Inc.

This paper fully develops a previous approach by George et al. (1993) to modeling uncertainty in class hierarchies. The model utilizes fuzzy logic to generalize equality to similarity which permitted impreciseness in data to be represented by uncertainty in classification. In this paper, the data model is formally defined and a nonredundancy preserving primitive operator, the merge, is described. It is proven that nonredundancy is always preserved in the model. An object algebra is proposed, and transformations that preserve query equality are discussed.

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently “rough” could be more easily implemented and maintained in the rough relational database.

Automatic programming is discussed in the context of software engineering. An approach to automatic programming is presented, which utilizes software engineering principles in the synthesis and maintenance of programs. As a simple demonstration, program-equivalent Turing machines are synthesized, encapsulated, reused, and maintained by genetic programming. Turing machines are synthesized from input-output pairs for a variety of simple problems. When a problem is solved, the solution is encapsulated and becomes part of a software library. The genetic program uses the library to solve new problems by combining library components with program primitives to synthesize new programs. When a new problem is solved or a known problem is solved more efficiently, the genetic program maintains the library so as to keep it valid and efficient.

A method is presented for transforming and combining heuristic knowledge gathered from multiple domain experts into a common semantic network representation. Domain expert knowledge is gathered with an interviewing tool based on personal construct theory. The problem of expressing and using a large body of knowledge is fundamental to artificial intelligence and its application to knowledge-based or expert systems. The semantic network is a powerful, general representation that has been used as a tool for the definition of other knowledge representations. Combining multiple approaches to a domain of knowledge may reinforce mutual experiences, information, facts, and heuristics, yet still retain unique, specialist knowledge gained from different experiences. An example application of the algorithm is presented in two separate expert domains.>

A research effort aimed at the development and unification of the prerequisite underlying theoretical foundations for an adequate approach to knowledge elicitation from repertory grid data is described. A theory of confirmation that incorporates the basic tenets of personal construct psychology directly into the logic as a basis for the determination of relevance is offered, thus strengthening the logic and extending personal construct psychology. These largely theoretical developments are applied to the representation and analysis of repertory grid data. The concept of an alpha -plane is introduced as a binary decomposition of repertory grid data that furnishes the realization of construct extensions (or ranges of convenience) needed to determine the range of relevance of a particular generalization or hypothesis. In addition, they provide the uniquely determined string of incidences required by any application of Bundy's truth functional incidence calculus. The theories are applied to the design and construction of NICOD-a semiautomated medical knowledge acquisition system. The system has been successfully employed in the elicitation of valuable heuristic radiological knowledge (mammography) that the domain experts (radiologists) were otherwise unable to articulate.>

An examination is made of the feasibility of higher-radix floating-point representations and, in particular, decimal-based representations. Traditional analyses of such representations have assumed the format of a floating-point datum to be roughly identical to that of traditional binary floating-point encodings such as the IEEE P754 task group standard representations. The authors relax this restriction and propose a method of encoding higher-radix floating-point data with range, precision, and storage requirements comparable to those exhibited by traditional binary representations. The results of other authors are extended to accommodate the proposed representation. A decimal alternative to traditional binary representations is proposed, and the behavior of such a system is contrasted with that of a comparable binary system.>

Programmers, even in well-organized software environments which utilize some modern software engineering practices, are often lacking of a discipline in their individual programming effort. There has not been an emphasis on discipline in progamming practice, as is traditional in other engineering and scientific fields' instruction. A framework organized to be suitable for early presentation and developing usage is presented and evaluated. It integrates the notions of top-down design, stepwise refinement, structured flowcharting, test case description, and analysis in the context of a framework for systematically developing and concurrently documenting programs. The framework was evaluated in actual usage during introductory programming instruction by comparing it to a typical conventional approach. A comparison of programming effort showed only a 16 percent increase in time required in the disciplined approach, which certainly makes it feasible for introductory instruction. Program quality comparisons were carried out by a comprehensive testing for logic errors in the completed projects. The results were impressively favorable for the disciplined approach.

This paper describes an approach that can introduce some of the concepts of software engineering to general business, engineering, and science students in an introductory FORTRAN programming course. The approach integrates the notions of top-down design, stepwise refinement, structured flowcharting, test case description, and analysis in the context of a methodology for systematically developing and documenting programs. Qualitative results from teaching these concepts are presented.

An algorithm is given for synthesizing a computer program from a trace of its behavior. Since the algorithm involves a search, the length of time required to do the synthesis of nontrivial programs can be quite large. Techniques are given for preprocessing the trace information to reduce enumeration, for pruning the search using a failure memory technique, and for utilizing multiple traces to the best advantage. The results of numerous tests are given to demonstrate the value of the techniques.