An Axiomatic Approach to Fuzzy Measures Like Set Cardinality for Finite Fuzzy Sets

Abstract

The aim of the paper is to propose an axiomatic system for fuzzy measures (denoted by fuzzy c-measures) like cardinality of sets for finite fuzzy sets that are defined in a universe of sets. The proposed axiomatic system is a generalization of the Casasnovas-Torrens axiomatic system introduced in [1]. We show a representation of fuzzy c-measures by a pair of special lattice homomorphisms and investigate several selected properties of fuzzy c-measure. © Springer-Verlag Berlin Heidelberg 2010.