The Credibility Theory And The Preliminary Research On Safe Stock

In classical set theory, an ordinary set is a unified whole which is composed of some elements. Each element either belongs to the set or not. However, this affiliation is not clear in many cases. For example, "young people", "about 100m" and so on. With the development of technology and human's deep cognition of nature and society, people's ability of cognizing and dealing with the uncertainty phenomenon in the real world improves gradually. In order to solve these uncertainty problems, Zadeh proposed the concept of fuzzy set through membership function in 1965. Nowadays, fuzzy set theory has made progress development. In order to measure a fuzzy event, Zadeh presented the concept of possibility and necessity measure in 1978 and 1979. After that, Liu and Liu proposed the concept of credibility measure in 2002. Thus, there are three kinds of measure in fuzzy mathematics: possibility measure, necessity measure, credibility measure. Traditionally, possibility measure is considered as the parallel concept of probability measure. However, it is the credibility measure which plays the role of probability measure in fuzzy set theory actually. This truth promotes the axiomatic system of credibility measure which called credibility theory. Liu established the axiomatic foundation of credibility theory in 2004. Presently, many scholars who study theory or application commit themselves into the research of credibility theory. In this paper we summarize and study the axiomatic foundation of credibility theory, and prove the variance formulas of two common types of fuzzy variable. We discuss the convergence of fuzzy sequence in credibility measure and deduce the central role of convergence in credibility. Then we give another equivalent theory of convergence in credibility. Credibility theory has not only theory value but also potential application prospects. In the forth part, we discuss how to determine the safety stock level of the node enterprise in a supply chain under fuzzy demand which was presented by Tan Yiman doctor.