Level Creditability of Fuzzy Numbers and its Properties

Making fuzzy information locally clarified by level cut-sets is a common method facing with many actual problems such as uncertainty optimization, fuzzy information processing and fuzzy control. Because all the discussions based on level cut-sets depend on its creditability, it has important theoretical and practical significance to establish a method for measuring the creditability of level cut-sets. In this paper, based on the Lebesgue measure of level cut-sets and the membership degree of an element in level cut-sets, we introduce the concept of level creditability of fuzzy numbers, present a necessary and sufficient condition of level creditability being equal to 1 for each lambdaepsi[0,1], and then consider the basic properties (such as continuity, monotonicity etc.) of level creditability and the integral properties of fuzzy numbers. In the last, we constitute the formulas computing the level creditability of triangular fuzzy numbers and trapezoid fuzzy numbers