Abstract
The fuzzy measures and fuzzy integrals for Zadeh's fuzzy sets were studied by Qiao and Wang [5, 6, 7, 12]. In this paper we consider the real-valued fuzzy measures and fuzzy integrals for L-fuzzy sets (where L is a pseudocomplemented infinitely distributive complete lattice). On a fuzzy σ-algebra of L-fuzzy sets, the concepts of fuzzy measure and fuzzy integral are introduced, some equivalent forms of fuzzy integrals on L-fuzzy sets are given. Moreover we discuss several properties of fuzzy integrals on L-fuzzy sets, and prove some convergence theorems for a sequence of fuzzy integrals on L-fuzzy sets.
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