The Relationship Between Two Types Of Fuzzy Probabilistic Sets And R-Fuzzy Sets And The Application In Fuzzy Risk Analysis

People often face the problem of how to deal with the randomness and ambiguity when dealing with the uncertainty problem.Fuzzy probabilistic sets consider both the randomness and the fuzziness,so more and more people pay attention to the research of fuzzy probabilistic sets.In this paper,we study fuzzy probabilistic sets from theory and application.The main research contents are as follows:1.In view of the close relationship between fuzzy probabilistic sets and random fuzzy sets(r-fuzzy sets),the definitions of three-valued r-fuzzy sets and five-valued r-fuzzy sets are proposed.Their relations with the bifuzzy probabilistic sets and interval intuitionistic fuzzy probabilistic sets are studied.Firstly,it is shown that there is a one-to-one relationship between three-valued r-fuzzy sets and r-intuitionistic fuzzy sets.Then,the concepts of the three-valued r-nested sets and the five-valued r-nested sets are given.It is proved that a bifuzzy probabilistic set is an equivalent class of a three-valued r-nested set,and a interval intuitionistic fuzzy set is an equivalent class of a five-valued r-nested set.2.Fuzzy risk analysis problem based on fuzzy probabilistic sets is studied.Firstly,it is shown that fuzzy risk analysis problems can be sorted by possibility degree method.Secondly,the new ranking method based on fuzzy probabilistic sets of fuzzy risk analysis problem is established.We give the ranking weight by applying the moments of fuzzy probabilistic sets to establish a new ranking method of fuzzy risk.Also,a simple example is analyzed to illustrate the proposed method.