Application of Fuzzy Logic to Social Choice Theory
1st Edition
Published on 3. March 2015
Book
Hardback
352 pages
978-1-4822-5098-5 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional Practice & Development
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 234 mm
Width: 160 mm
Thickness: 25 mm
Weight
635 gr
ISBN-13
978-1-4822-5098-5 (9781482250985)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
John N. Mordeson | Davender S. Malik | Terry D. Clark
Application of Fuzzy Logic to Social Choice Theory
Book
11/2019
1st Edition
Chapman & Hall/CRC
€96.50
Shipment within 15-20 days
John N. Mordeson | Davender S. Malik | Terry D. Clark
Application of Fuzzy Logic to Social Choice Theory
E-Book
03/2015
Chapman & Hall/CRC
€89.99
Available for download
John N. Mordeson | Davender S. Malik | Terry D. Clark
Application of Fuzzy Logic to Social Choice Theory
E-Book
03/2015
Chapman and Hall
€89.99
Available for download
Persons
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.
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.
Content
Fuzzy Maximal Subsets. Fuzzy Choice Functions. Factorization of Fuzzy Preference Relations. Fuzzy Non-Arrow Results. Fuzzy Arrow's Theorem. Single Peaked Fuzzy Preferences: Black's Median Voter Theorem. Rationality. Arrow-Type Results under Intuitionistic Fuzzy Preferences. Manipulability of Fuzzy Social Choice Functions. Similarity of Fuzzy Choice Functions. Index.