Fuzzy Choice Functions
Fuzzy Choice Functions

Author: Irina Georgescu

Publisher: Springer

Published: 2007-07-16

Total Pages: 286

ISBN-13: 3540689982

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This book extends the theory of revealed preference to fuzzy choice functions, providing applications to multicriteria decision making problems. The main topics of revealed preference theory are treated in the framework of fuzzy choice functions. New topics, such as the degree of dominance and similarity of vague choices, are developed. The results are applied to economic problems where partial information and human subjectivity involve vague choices and vague preferences.

Application of Fuzzy Logic to Social Choice Theory
Application of Fuzzy Logic to Social Choice Theory

Author: John N. Mordeson

Publisher: CRC Press

Published: 2015-03-03

Total Pages: 346

ISBN-13: 1482250993

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Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy max

Fuzzy Social Choice Theory
Fuzzy Social Choice Theory

Author: Michael B. Gibilisco

Publisher: Springer

Published: 2014-02-24

Total Pages: 196

ISBN-13: 3319051768

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This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem and the median voter theorem. After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a social choice that can be both strategy-proof and non-dictatorial. Moreover, the median voter theorem is shown to hold under strict fuzzy preferences but not under weak fuzzy preferences. By providing a standard model of fuzzy social choice and by drawing the necessary connections between the major theorems, this book fills an important gap in the current literature and encourages future empirical research in the field.

Towards the Future of Fuzzy Logic
Towards the Future of Fuzzy Logic

Author: Rudolf Seising

Publisher: Springer

Published: 2015-05-26

Total Pages: 382

ISBN-13: 3319187503

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This book provides readers with a snapshot of the state-of-the art in fuzzy logic. Throughout the chapters, key theories developed in the last fifty years as well as important applications to practical problems are presented and discussed from different perspectives, as the authors hail from different disciplines and therefore use fuzzy logic for different purposes. The book aims at showing how fuzzy logic has evolved since the first theory formulation by Lotfi A. Zadeh in his seminal paper on Fuzzy Sets in 1965. Fuzzy theories and implementation grew at an impressive speed and achieved significant results, especially on the applicative side. The study of fuzzy logic and its practice spread all over the world, from Europe to Asia, America and Oceania. The editors believe that, thanks to the drive of young researchers, fuzzy logic will be able to face the challenging goals posed by computing with words. New frontiers of knowledge are waiting to be explored. In order to motivate young people to engage in the future development of fuzzy logic, fuzzy methodologies, fuzzy applications, etc., the editors invited a team of internationally respected experts to write the present collection of papers, which shows the present and future potentials of fuzzy logic from different disciplinary perspectives and personal standpoints.

Fuzziness and Approximate Reasoning
Fuzziness and Approximate Reasoning

Author: Kofi Kissi Dompere

Publisher: Springer

Published: 2009-07-28

Total Pages: 311

ISBN-13: 3540880879

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We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The “degree” of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.

Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations

Author: Jesús Medina

Publisher: Springer

Published: 2018-05-30

Total Pages: 773

ISBN-13: 3319914766

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This three volume set (CCIS 853-855) constitutes the proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2017, held in Cádiz, Spain, in June 2018. The 193 revised full papers were carefully reviewed and selected from 383 submissions. The papers are organized in topical sections on advances on explainable artificial intelligence; aggregation operators, fuzzy metrics and applications; belief function theory and its applications; current techniques to model, process and describe time series; discrete models and computational intelligence; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy logic and artificial intelligence problems; fuzzy mathematical analysis and applications; fuzzy methods in data mining and knowledge discovery; fuzzy transforms: theory and applications to data analysis and image processing; imprecise probabilities: foundations and applications; mathematical fuzzy logic, mathematical morphology; measures of comparison and entropies for fuzzy sets and their extensions; new trends in data aggregation; pre-aggregation functions and generalized forms of monotonicity; rough and fuzzy similarity modelling tools; soft computing for decision making in uncertainty; soft computing in information retrieval and sentiment analysis; tri-partitions and uncertainty; decision making modeling and applications; logical methods in mining knowledge from big data; metaheuristics and machine learning; optimization models for modern analytics; uncertainty in medicine; uncertainty in Video/Image Processing (UVIP).

Fuzzy Rationality
Fuzzy Rationality

Author: Kofi Kissi Dompere

Publisher: Springer Science & Business Media

Published: 2009-03-20

Total Pages: 301

ISBN-13: 3540880828

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Philosophy involves a criticism of scientific knowledge, not from a point of view ultimately different from that of science, but from a point of view less concerned with details and more concerned with the h- mony of the body of special sciences. Here as elsewhere, while the older logic shut out possibilities and imprisoned imagination within the walls of the familiar, the newer logic shows rather what may happen, and refuses to decide as to what must happen. Bertrand Russell At any particular stage in the development of humanity knowledge comes up against limits set by the necessarily limited character of the experience available and the existing means of obtaining knowledge. But humanity advances by overcoming such limits. New experience throws down the limits of old experience; new techniques, new means of obtaining knowledge throw down the limits of old techniques and old means of obtaining knowledge. New limits then once again appear. But there is no more reason to suppose these new limits absolute and final than there was to suppose the old ones absolute and final.