큐빅 피타고라스 퍼지집합에 기반을 둔 퍼지 공학시스템 신뢰도 분석
Reliability Analysis of Fuzzy Engineering Systems Based on Cubic Pythagorean Fuzzy Sets
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초록
공학시스템을 설계 및 운용할 경우에 이 시스템의 신뢰도는 중요한 이슈가 된다. 즉, 불확실성과 부정확함을 다루는 것이 필요한다는 것을 의미한게 된다. 이러한 모호함을 포함하고 있는 시스템의 신뢰도를 다루는 방법이 퍼지집합이론이다. 퍼지집합은 0과 1사이의 실수로 소속정도를 표현한다. 직관퍼지집합은 소속정도와 비소속정도를 각각 0과 1사이의 실수로 표현한다. 피타고라스 퍼지집합은 소속정도와 비소속정도의 합이 1을 초과하는 문제를 해결한 퍼지집합이다. 구간값 피타고라스 퍼지집합은 피타고라스 퍼지집합의 상한과 하한을 구간으로 표현한 집합이다. 큐빅집합은 구간값 퍼지집합과 퍼지지합의 쌍으로 표현한다. 큐빅집합은 매개변수를 구간으로 분석을 할 경우 하나의 매개변수를 다룰 수 있는 방법을 제공한다. 또한 큐비 피타고라스 퍼지집합은 구간값 피타고라스 퍼지집합과 피타고라스 퍼지집합의 쌍으로 표현하므로 소속정도와 비소속정도의 합이 1을 초과하는 문제는 발생하지 않는다. 본 연구에서는 큐빅 피타고라스 퍼지집합을 기반으로 하여 퍼지공학시스템의 신뢰도를 평가하는 방법을 제안한다. 큐빅 피타고라스 퍼지집합은 주어지는 조건에 따라 큐빅집합, 피타고라스 퍼지집합 등으로 축약할 수 있다. 그러므로 큐빅 피타고라스 퍼지집합을 사용한 방법은 이들의 방법을 모두 함의 한다고 할 수 있다.
Abstract
When designing and operating engineering systems, the reliability of these systems become an important issue. This means that it is necessary to deal with uncertainty and uncorrectness. Fuzzy set theory provide a way to deal with the reliability of systems containing such ambiguity. Fuzzy sets express the belongingness degree as a real number between 0 and 1. Intuitionistic fuzzy sets describe the belongingness degree and non-belongingness degree as real number between 0 and 1, respectively. Pythagorean fuzzy sets are a fuzzy set that solves the problem where the sum of the belongingness degree and non-belongingness degree exceeds 1. Interval-valued Pythagorean fuzzy sets are a set that expresses the upper and lower limits of the Pythagorean fuzzy set as intervals. cubic sets are expressed as the pair of an interval-valued fuzzy set and a fuzzy set. Cubic sets provide a way to handle a single parameter when analyzing the parameter as a interval. In addition, the Cubic Pythagorean fuzzy sets are expressed as a pair of an interval-valued Pythagorean fuzzy set and a Pythagorean fuzzy set, so the problem that the sum of the belongingness degree and non-belongingness degree exceeds 1 does not occur. In this study, we propose a method to evaluate the reliability of fuzzy engineering systems based on cubic Pythagorean fuzzy sets. Cubic Pythagorean fuzzy sets can be reduced to cubic sets, Pythagorean fuzzy sets, etc. depending on given conditions. Therefore, it can be said that the method using the cubic Pythagorean fuzzy set implies all of these methods.
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