On the defect of additivity of fuzzy measures

Authors:
A. I. Ban;S. G. Gal
Affiliations:
Department of Mathematics, University of Oradea, str. Armatei Române 5, 3700 Oradea, Romania;Department of Mathematics, University of Oradea, str. Armatei Române 5, 3700 Oradea, Romania
Venue:
Fuzzy Sets and Systems - Mathematics
Year:
2002

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Abstract

It is well-known that fuzzy measures are non-additive. In this paper we introduce the concept of defect which gives us the degree of non-additivity of fuzzy measures. For large classes of fuzzy measures this defect is calculated and estimated. Three kinds of applications are given: to the approximative calculation of some fuzzy integrals, to the best approximation of a fuzzy measure by classical measures and to the introduction of an invariant at translations distance on the set of fuzzy measures.