Fuzzy System Reliability Analysis Using q-rung Orthopair Fuzzy Sets
Fuzzy set theory introduced by Zadeh has been very successful in dealing with vagueness and uncertainty in various fields. In the fuzzy set, each element of universe belongs to the fuzzy concept with a degree of membership in the unit interval [0, 1]. In order to overcome the problem of fuzzy sets expressing the degree of membership as only one real number, various extensions of fuzzy sets have been developed by many researchers: interval-valued fuzzy sets, intuitionistic fuzzy sets, vague sets, neutrosophic sets, hesitant fuzzy sets, Pythagorean fuzzy sets, orthopair fuzzy sets, etc. In interval-valued fuzzy sets proposed by Tursen, the degree of membership is expressed as a closed subinterval of [0, 1]. Intuitionistic fuzzy sets introduced by Atanassov allow us to represent the degree of membership as truth degree of membership and falsity degree of membership, and the sum of them is limited to 1. Gau et al. also explained vague sets that describe the degree of membership as subinterval. Bustince et al. has proved that these sets are mathematically equivalent to intuitionistic fuzzy sets. In neutrosophic sets proposed by Smarandache, the degree of membership is consisted of truth degree of membership, indeterminacy degree of membership, and falsity degree of membership, and then the indeterminacy is quantified explicitly. Torra introduced hesitant fuzzy sets in which the degree of membership is described by a set of possible values. In the Pythagorean fuzzy set proposed by Yager et al., to solve the problem that the sum of the truth degree of membership and the falsity is greater than one, each degree of membership is squared so that the sum of them is one or less. Orthpair fuzzy set proposed by Yager allow us to express the degree of membership as the q-th power of truth degree of membership and the q-th power of falsity degree of membership. The sum of them is bounded by one. These sets are called the q-rung orthopair fuzzy sets(q-ROFSs). If q = 1, q-ROFSs degenerates to an intuitionistic fuzzy sets and if q = 2, to a Pythagorean fuzzy sets. In this paper, we propose a method for calculating the reliability of fuzzy systems using q-ROFSs which are the generalization of the degree of membership expressed as intervals. Since this method uses the q-ROFS with generalized intervals, it is possible to calculate the reliability of systems more flexibly than the other approaches.