Fuzzy System Reliability Analysis Using Picture Fuzzy Sets
Reliability analysis is the important discipline of reliability engineering. In conventional reliability analysis, the reliability of the components of a system is represented as exact values. Obtaining these data under changing environment conditions is often difficult. Hence fuzzy set theory is used to analyze the fuzzy system reliability, where the reliabilities of the components of a system are represented by fuzzy sets. There are various types of fuzzy sets used to evaluate the reliability of the systems such as the fuzzy sets, interval valued fuzzy sets, intutionistic fuzzy sets, picture fuzzy sets. In the fuzzy sets, the degree of membership is represented as a real number. In the interval valued fuzzy sets, the degree of membership is represented as an interval [, ], where is the minimum degree of membership and is the maximum degree of membership. [, ] ⊆ . In the intuitionistic fuzzy sets, the degree of membership consist of and , where is the degree of membership and is the degree of non-membership. , ∈ . In the picture fuzzy sets, the degree of membership consist of , , and , where is called the degree of positive membership, is called the degree of neutral membership, and is called the degree of negative membership. , , ∈ . In this paper we propose the way to analyze the fuzzy system reliability based on the picture fuzzy sets. The picture fuzzy sets have the capability of representing the positive, negative, neutral, and refusal situation. Therefore the picture fuzzy sets become more flexible to describe the reliabilities than the other methods.