구간값 피타고라스 퍼지집합에 기반을 둔 퍼지 공학시스템 신뢰도 분석
Reliability Analysis of Fuzzy Engineering Systems Based on Interval-Valued Pythagorean Fuzzy Sets
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초록
실세계에서 운용하는 공학시스템의 신뢰도는 중요한 의미를 가진다. 이러한 신뢰도는 부정확한 데이터, 잘못된 조작 등으로 정확한 신뢰도를 구하는 것이 어려워 진다. 이러한 문제를 해결하기 위해 퍼지집합을 사용하기 시작하였다. 신뢰도를 계산하는데 사용하는 퍼지집합은 다음과 같이 여러 가지가 있다. 퍼지집합에서는 퍼지집합의 소속정도 인 실수로 표현한다. 여기에서 ∈ . 직관 퍼지집합에서는 퍼지집합의 소속정도는 로 비소속정도는 로 각각 표현한다. 여기에서 , ∈ , 0 ≤ + ≤ 1. 구간값 직관 퍼지집합에서는 퍼지집합의 소속정도는 [, ]로 비소속정도는 [, ]로 각각 표현한다. 여기에서 , , , ∈ , + ≤ 1, 0 ≤ + ≤ 1, 0 ≤ + ≤ 1. 피타고라스 퍼지집합에서 퍼지집합의 소속정도는 와 비소속정도는 로 표현한다. 여기에서 , ∈ , 0 ≤ + ≤ 1. 본 논문에서는 피타고라스 퍼지집합에 유연성을 표현할 수 있는 구간값 피타고라스 퍼지집합을 이용하여 퍼지 공학시스템의 신뢰도를 계산하는 방법을 제안한다.
Abstract
The reliability of the engineering systems operating in the real world has an important meaning. Such reliability becomes difficult to obtain an accurate reliability due to inaccurate data, wrong manipulation, etc. To solve this problems, the fuzzy sets have been used. There are several fuzzy sets used to calculate reliability. In the fuzzy sets, it is expressed as a real number , which is the belongingness degree of the fuzzy set. ∈ . In the intuitionistic fuzzy sets, the belongingness degree of the fuzzy set is expressed as , and the non-belongingness degree is described as respectively. , ∈ , 0 ≤ + ≤ 1. In the interval-valued intuitionistic fuzzy sets, the belongingness degree of the fuzzy set is expressed as [, ] and the non-belongingness degree is represented as [, ] respectively. , , , ∈ , + ≤ 1, 0 ≤ + ≤ 1, 0 ≤ + ≤ 1. In the Pythagorean fuzzy sets, the belongingness degree in a fuzzy set is expressed as , and the non-belongingness degree is expressed as . , ∈ , 0 ≤ + ≤ 1. In this paper, we propose a method for calculating the reliability of the fuzzy engineering systems using the interval-valued Pythagorean fuzzy sets that can express flexibility in the Pythagorean fuzzy sets.
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