Logika preferencija na grubim i rasplinutim skupovima

Abstract

Theories of fuzzy sets and rough sets, as alternatives to the usual set theory founded on the two valued classical logic, present an appropriate context for developing the basic notions of the logic of preference and consequently, of the social choice theory. In this paper we present an introductory survey of two non-classical concepts of set: fuzzy set and rough set, as originally introduced by L. A. Zadeh and Z. Pawlak respectively, and then we prove that a preference relation defined by means of rough sets has the same basic properties as the classical or the fuzzy one. Moreover, we prove that The Liberal Paradox, as originally formulated by A. Sen, holds in the framework of theory of rough sets as well.