Janusz Kacprzyk

Distances between intuitionistic fuzzy sets

A geometrical representation of an intuitionistic fuzzy set is a point of departure for our proposal of distances between intuitionistic fuzzy sets. New definitions are introduced and compared with the approach used for fuzzy sets. It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances.

Group decision making with a fuzzy linguistic majority

Abstract The determination of solutions in group decision making is considered. The point of departure is a collection of individual fuzzy preference relations. A solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation. As opposed to conventional approaches in which a crisp (threshold type) majority rule is used, we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier, e.g., ‘most’, ‘much more than 50%’, etc. A calculus of linguistically quantified propositions is applied. Using the fuzzy majority, various solution concepts are derived, mainly of the type of core, minimax (opposition) set and consensus winner.

Entropy for intuitionistic fuzzy sets

Abstract A non-probabilistic-type entropy measure for intuitionistic fuzzy sets is proposed. It is a result of a geometric interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them proposed in Szmidt and Kacprzyk (to appear). It is also shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .

Group decision making and consensus under fuzzy preferences and fuzzy majority

Abstract We present how fuzzy logic with linguistic quantifiers, mainly its calculi of linguistically quantified propositions, can be used in group decision making. The fuzzy linguistic quantifiers (exemplified by most, almost all,...) are employed to represent a fuzzy majority which is in many cases closer to a real human perception of the very essence of majority. Fuzzy logic provides here means for a formal handling of such a fuzzy majority which was not possible by using traditional formal apparata. Assuming fuzzy individual and social preference relations, as it is commonly done, and employing in addition a fuzzy majority expressed by a fuzzy linguistic quantifier, we redefine solution concepts in group decision making, and present new ‘soft’ degrees of consensus.

Computing with Words in Information/Intelligent Systems 1

M. Sugeno: Foreword.- Neuro-Fuzzy and Genetic Systems for Computing with Words: S. Mitaim, B. Kosko: Neural Fuzzy Intelligent Agents S. Siekmann, R. Neuneier, H.-G. Zimmermann, R. Kruse: Neuro Fuzzy Systems for Data Analysis J. Leski, E. Czogala: A New Fuzzy Interference System Based on Artificial Neural Network and its Applications O. Cordon, A. Gonzales, F. Herrera, R. Perez: Encouraging Cooperation in the Genetic Iterative Rule Learning Approach for Qualitative Modeling.- Tools for Linguistic Data Modeling and Analysis: H. Lee, H. Tanaka: Fuzzy Graphs with Linguistic Input-Outputs by Fuzzy Approximation Models M.A. Gil, P.A. Gil, D.A. Ralescu: Fuzzy Random Variables: Modeling Linguistic Statistical Data.- Linguistic Models in System Reliability, Quality Control and Risk Analysis: T. Onisawa, A. Ohmori: Linguistic Model of System Reliability Analysis P. Grzegorzewski, O. Hryniewicz: Lifetime Tests for Vague Data C. Huang, D. Ruan: Systems Analytic Models for Fuzzy Risk Estimation.- Linguistic Models in Decision Making, Optimization and Control: H. Kiendl: Decision Analysis by Advanced Fuzzy Systems J. kacprzyk, H. Nurmi, M. Fedrizzi: Group Decision Making and a Measure of Consensus under Fuzzy Preferences and a Fuzzy Linguistic Majority S. Chanas, D. Kuchta: Linear Programming with Words J.J. Buckley, T. Feuring: Computing with Words in Control R. Kowalczyk: On Linguistic Fuzzy Constraint Satisfaction Problems.- Linguistic and Imprecise Information in Databases and Information Systems: G. Chen: Data Models for Dealing with Linguistic and Imprecise Information F.E. Petry, M. Cobb, A. Morris: Fuzzy Set Approaches to Model Uncertainty in Spatial Data and Geographic Information Systems J.C. Cubero, J.M. Medina, O.Pons, M.A. Vila: Computing Fuzzy Dependencies with Linguistic Labels J. Kacprzyk, S. Zadrozny: The Paradigm of Computing with Words in Intelligent Database Querying W. Pedrycz: Lingusitic Data Mining R.A. Bustos, T.D. Gedeon: Evaluation of Connectionist Information Retrieval in a Legal Document Collection.- Applications. Information in Databases and Information Systems: M.E. Cohen, D.L. Hudson: Using Linguistic Models in Medical Decision Making J.M. Mendel, S. Murphy, L.C. Miller, M. Martin, N. Karnik: The Fuzzy Logic Advisor for Social Judgements: A First Attempt J. Zelger, A.G. de Wet, A.-M. Pothas, D. Petkov: Conceptualisation with GABEK: Ideas on Social Change in South Africa F. Herrera, E. Lopez, C. Manadana, M. Rodriguez: A Linguistic Decision Model to Suppliers Selection in International Purchasing L. Zerrouki, B. Bouchon-Meunier, R. Fondacci: Fuzzy System for Air Traffic Flow Management G. Michalik, W. Mielczarski: A Fuzzy Approach to Contracting Electrical Energy in Competitive Electricity Markets D. Ruan: Fuzzy Logic and Intelligent Computing in Nuclear Engineering A. Filippidis, L.C. Jain, N.M. Martin: Computational Intelligence Techniques in Landmine Detection.

A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences

Abstract Consensus, as traditionally meant to be a full and unanimous agreement, is often not reachable in practice. A degree of consensus for indicating how far a particular group of individuals is from consensus may be therefore very useful. We propose a new measure (degree) of consensus which is more human-consistent in the sense that it better reflects a real human perception of the essence of consensus in practice. Basically, our consensus measure expresses the degree to which, say, ‘most of the important individuals agree as to (their testimonies concerning) almost all of the relevant options’. The point of departure is the set of individual testimonies which are here the individual fuzzy preference relations. As a formal tool we use a fuzzy-logic-based calculus of linguistically quantified propositions.

Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology.Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.

A consensus-reaching process under intuitionistic fuzzy preference relations

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.

Advances in Web Intelligence

Web Intelligence (WI) presents excellent opportunities and challenges for the research and development of new generation of Webbased information processing technology, as well as for exploiting Webbased advanced applications. Based on two perspectives of WI research: an intelligent Web-based business-centric schematic diagram and the conceptual levels of WI, we investigates various ways to study WI and potential applications.

Computing with words in intelligent database querying: standalone and internet-based application

Abstract We present how computing with words, meant as a set of fuzzy-logic-based tools for an effective and efficient handling of imprecise elements of natural language, can be implemented for fuzzy querying via a user-friendly interface to Microsoft Access, FQUERY for Access. The system accommodates fuzzy (imprecise) terms and linguistic quantifiers allowing for queries exemplified by “find (all) records such that most of the (important) clauses are satisfied (to a degree from [0,1])”. L.A. Zadehs [Comput. Math. Appl. 9 (1983) 149] fuzzy logic based calculus of linguistically quantified propositions, and R.R. Yagers [IEEE Trans. Syst. Man Cybernet. 18 (1988) 183] ordered weighted averaging (OWA) operators are employed to deal with fuzzy linguistic quantifiers. It is then shown how FQUERY for Access, which is a standalone application, may be extended to support fuzzy querying via the Internet (or, analogously, Intranet). It is shown how WWW browsers, both the Netscape Navigator and Microsoft Explorer, can be employed for developing a fuzzy querying interface for handling imprecise natural language elements in database queries following Zadehs computing with words paradigm.