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Application of Fuzzy Logic to Social Choice Theory
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John N. Mordeson (Creighton University, Omaha, Nebraska, USA) Davender S. Malik (Creighton University, Omaha, Nebraska, USA)
Application of Fuzzy Logic to Social Choice Theory by John N. Mordeson (Creighton University, Omaha, Nebraska, USA) at Abbey's Bookshop,

Application of Fuzzy Logic to Social Choice Theory

John N. Mordeson (Creighton University, Omaha, Nebraska, USA) Davender S. Malik (Creighton University, Omaha, Nebraska, USA) Terry D. Clark (Creighton University, Omaha, Nebraska, USA)


Apple Academic Press Inc.

Mathematical logic;
Fuzzy set theory;
Algorithms & data structures


352 pages

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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 maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the union (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's theorem, and Black's median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard-Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu's degree of similarity of two fuzzy choice functions.

By:   John N. Mordeson (Creighton University Omaha Nebraska USA), Davender S. Malik (Creighton University, Omaha, Nebraska, USA), Terry D. Clark (Creighton University, Omaha, Nebraska, USA)
Imprint:   Apple Academic Press Inc.
Country of Publication:   Canada
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 25mm
Weight:   612g
ISBN:   9781482250985
ISBN 10:   1482250985
Series:   Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Pages:   352
Publication Date:   March 2015
Audience:   College/higher education ,  College/higher education ,  Further / Higher Education ,  Primary
Format:   Hardback
Publisher's Status:   Active

Fuzzy Maximal Subsets Fuzzy Set Theory Fuzzy Maximal Sets Fuzzy Choice Functions Basic Properties Consistency Conditions M-Rationality and G-Rationality Full Rationality of Fuzzy Choice Functions on Base Domain Quasi-Transitive Rationality of Fuzzy Choice Functions Full Rationality and Congruence Axioms of Fuzzy Choice Functions Factorization of Fuzzy Preference Relations Basic Definitions and Results Quasi-Subtraction Factorizations Intuitionistic Fuzzy Relations Intuitionistic Fuzzy Preference Relations and Their Factorization Fuzzy Non-Arrow Results Nondictatorial Fuzzy Aggregation Rules Auxiliary Functions Arrow's Theorem and Max-Star Transitivity Fuzzy Arrow's Theorem Dictatorial Fuzzy Preference Aggregation Rules Representation Rules, Veto Players, Oligarchies, and Collegiums Decisive Sets, Filters, and Fuzzy Arrow's Theorem Fuzzy Preferences and Social Choice Fuzzy Preferences and Arrow-Type Problems The Structure of Fuzzy Preferences: Social Choice Implications Single Peaked Fuzzy Preferences: Black's Median Voter Theorem Fuzzy Aggregation Preference Rules Fuzzy Voting Rules Single-Peaked Fuzzy Profiles The Core in Fuzzy Spatial Models Rationality Fuzzy Preference and Preference-Based Choice Functions Fuzzy Choice Functions, Revealed Preference and Rationality Arrow-Type Results under Intuitionistic Fuzzy Preferences Fuzzy Preference Profiles and Fuzzy Aggregation Rules IIA3 and Nondictatorial Fuzzy Aggregation Rules IIA2, IIA4, and Fuzzy Arrow's Theorem Representation Rules, Veto Players, and Oligarchies Fuzzy Preference and Arrowian Results Intuitionistic Arrow's Theorem and Gibbard's Oligarchy Theorem Manipulability of Fuzzy Social Choice Functions Preliminaries Fuzzy Social Choice Functions Impossibility Results Non-Manipulable Partitioning Application Similarity of Fuzzy Choice Functions Fuzzy Choice Functions Similarity of Fuzzy Choice Functions Arrow Index of a Fuzzy Choice Function Index Exercises and References appear at the end of each chapter.

Dr. John N. Mordeson is a professor of mathematics, the John N. Mordeson Endowed Chair in Mathematics, and the director of the Center for Mathematics of Uncertainty at Creighton University. Dr. Mordeson has published 15 books and nearly 200 journal articles. He is an editorial board member of numerous journals and the current president of the Society for Mathematics of Uncertainty. His research interests include coding theory, fuzzy automata theory, fuzzy information retrieval, and fuzzy cluster analysis. Dr. Davender S. Malik is a professor of mathematics at Creighton University. His research interests include algebra, fuzzy automata theory, and fuzzy logic. Dr. Malik has published 17 books and more than 50 papers. Dr. Terry D. Clark is a professor of political science and the director of the graduate program in international relations at Creighton University. Dr. Clark has published four books and numerous journal articles. His research interests include fuzzy math spatial modeling, comparative politics, international relations, social network analysis, and intelligence analysis.

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