格值测度和格值积分

Lattice Value Measure and Lattice Integration

本文首先把Fuzzy测度的度集从实数集推广到δ-完全格L上,形成L-Fuzzy测度概念。然后与零可加、零上连续、自连续等概念连系,探讨了L-Fuzzy测度概念中的连续性与这些概念的关系。在L-Fuzzy测度基础上,本文将Fuzzy积分推广为积分值为格值的L-Fuzzy积分,并探讨了L-Fuzzy积分的基本性质。

In this paper, we extend the concept of fuzzy measure to L-fuzzy ineasure, where,the values of L-fuzzy measure are generally elements of lattice.We approach the ralations between continuity of L-fuzzy measure and some other concepts, such as, zero additivity, autocontinuity, etc. Based on the concept of L-fuzzy measure, we extend the concept of fuzzy integration to L-fuzzy integration, where, the values of L-fuzzy integration are elements of lattice. The basic charactors of L-fuzzy integration are discussed in the paper.