“K23798” 2015/2/2
This book provides a comprehensive study of fuzzy social choice theory. Hu-
man thinking is marked by imprecision and vagueness. These are the very
qualities that fuzzy logic seeks to capture. Thus, social choice theory suggests
itself as a means for modeling the uncertainty and imprecision endemic in
social life. Nonetheless, fuzzy logic has seen little application in the social sci-
ences to include social choice theory. We attempt to partially fill this lacuna.
The main focus of Chapter 1 is the concept of a fuzzy maximal subset of
a set of alternatives X. A fuzzy maximal subset gives the degree to which the
elements of X are maximal with respect to a fuzzy relation on X and a fuzzy
subset of X. This allows for alternative notions of maximality not allowed in
the crisp case. The main result states that a fuzzy maximal subset is not the
zero function if and only if the fuzzy preference relation involved is partially
Chapter 2 deals with fuzzy choice functions. Classical revealed preference
theory postulates a connection between choices and revealed preferences. If it
is assumed that preferences of a set of individuals are not cyclic, then their col-
lective choices are rationalizable. We examine this question in some detail for
the fuzzy case. We determine conditions under which a fuzzy choice function
is rationalizable. We also present results inspired by Georgescu [24]. Desai [16]
characterized the rationality of fuzzy choice functions with reflexive, strongly
connected, and quasi-transitive rationalization in terms of path independence
and the fuzzy Condorcet property. We consider these results as well as those
of Chaudhari and Desai [11] on various types of rationality.
Chapter 3 is concerned with the factorization of a fuzzy preference rela-
tion into the “union” of a strict fuzzy relation and an indifference operator,
where union here means conorm. Such a factorization was motivated by Fono
and Andjiga [12]. The factorization is useful in the examination of Arrowian
type results. We show that there is an inclusion reversing correspondence be-
tween conorms and fuzzy strict preference relations in factorizations of fuzzy
preference relations into their strict preference and indifference components.
In Chapter 4, we consider fuzzy non-Arrowian results. The first author
felt that presenting this material before Arrowian type results would help
emphasize the difference between the fuzzy case and the crisp case. We pro-
vide two types of fuzzy aggregation rules that satisfy certain fuzzy versions of

Get Application of Fuzzy Logic to Social Choice Theory now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.