Study on fuzzy risk analysis based on fuzzy numbers

Abstract

Fuzzy set theory 1965 is a powerful tool to deal with real-life situations. Real numbers can be linearly ordered by ≤ or ≥; however, this type of inequality does not exist in fuzzy numbers. Since fuzzy numbers are represented by possibility distribution, they can overlap with each other and it is difficult to determine clearly whether one fuzzy number is larger or smaller than the other. An efficient approach for ordering the fuzzy numbers is by using a ranking function, where is a set of fuzzy numbers defined on the real line, where a natural order exists. Thus, specific ranking of fuzzy numbers is an important procedure for decision making in a fuzzy environment and, generally, has become one of the main problems in fuzzy set theory. It is obvious that we often face the difficulty of lacking precise information to assess the risk of component made by a manufactory in an uncertain environment. In order to overcome this problem, fuzzy number have been used to represent the fuzziness of evaluating value in fuzzy risk analysis problem, where the task of ranking fuzzy number is very important.