F集上的可能性测度与一致信任函数扩张全体的半格结构

SEMI-LATTICE STRUCTURE OF ALL EXTENSIONS OF POSSIBILITY MEASURE AND CONSONANT BELIEF FUNCTION ON THE FUZZY SET

本文提出了Fuzzy集合上的可能性测度与一致信任函数两个概念,并得到可能性测度扩张与一致信任函数扩张两个重要定理,同时,还讨论了扩张全体的代数结构。

In this paper, we introduce the concepts: possibility measure and consonant belief function on the set of all fuzzy subsets of X, P-consistent and B-consistent of set function, and give a necessary and sufficient condition for that a mapping μ from an arbitrary nonempty class C of a fuzzy subsets of X into the unit interval [0, 1] can be extended to a possibility measure on the set of all fuzzy subsets of X, and analogously, a necessary and sufficient condition for extending to a consonant belief function. We discuss also the algebraic structure of all of extensions.