Application of Fuzzy Logic to Social Choice Theory

Focuses on one of the most important discoveries in social theory: Arrow’s theorem Emphasizes the difference between the fuzzy case and the crisp case Shows how Black’s median voter theorem solves the Arrowian impossibility theorem by restricting preferences to single-peaked profiles Obtains Arrow-type results using an involutive fuzzy complement Presents many results based on the work of Georgescu, Desai, Chaudhari, Fono, Andjiga, Duddy, Perote-Pena, Piggins, Dutta, Banerjee, Barrett, Pattanaik, Salles, Nana, Abdelaziz, Figueria, and Meddeb Summary 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.

• ISBN: 9781482250985
• Editorial: CHAPMAN & HALL LTD.
• Encuadernacion: Tela
• Páginas: 352
• Fecha Publicación: 03/03/2015
• Nº Volúmenes: 1
• Idioma: