부산대학교 도서관

In this paper we study the problem of constructing a Sugeno measure m ̄ on a suitable family S ̃ of fuzzy subsets of a space Ω. More precisely, we suppose that there exists a measure m on a crisp measurable space (Ω, S) , we request that all the α-cuts of the elements of S ̃ belong to the algebra S of the measurable crisp subsets and we suppose that the membership function assumes only finitely many values α 1,…,α n . Under these hypotheses we construct the measure m ̄ ( A ̃ ) of the fuzzy set A ̃ in terms of the measure m(A i) of its α-cuts A i, i=1,…,n , in the case where both m ̄ and m are decomposable.