Abstract
This work deals with the hesitant fuzzy number and averaging operator and fuzzy reliability with the help of Weibull lifetime distribution. Fuzzy reliability function and triangular hesitant fuzzy number also computed with α-cut set of the proposed reliability function. After applying the averaging operator of hesitant theory, the results are better than simple fuzzy. Also at last, a numerical example has been shown that how the hesitant fuzzy and α-cut work in case of reliability theory.
Highlights
Reliability theory plays a key role in the history of fuzzy set theory and engineering fields
Zadeh (1965) presented the theory of fuzzy set which is a group of objects with a continuum class of membership function and these sets are characterized by its membership function, which has every membership defined between zero and one of each class
A method has been proposed for computing fuzzy reliability function and its α-cut sets and discussed fuzzy reliability function for the series system, parallel system and k-out-of-n system
Summary
Reliability theory plays a key role in the history of fuzzy set theory and engineering fields. They proposed summation of series operators for the hesitant fuzzy set and discussed some basic operations and summation operators for the hesitant fuzzy set. A method has been proposed for computing fuzzy reliability function and its α-cut sets and discussed fuzzy reliability function for the series system, parallel system and k-out-of-n system. Hesitant fuzzy set have widely used in real life such as decision-making, medical diagnosis and information retrieval .Kumar et al (2017) discussed the fuzzy reliability of series, parallel and consecutive-k-out-of-n:F system of non-identical components using hesitant fuzzy set theory and aggregation operators with the help of Weibull distribution. A fuzzy set Z is defined by its membership function Z : Y 0,1 , where Z (Y ) is the degree of membership component of z in a fuzzy set Y for all y Y
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