너비를 고려한 수준 (λ, 1) 구간값 퍼지집합을 이용한 시스템의 신뢰도 분석
Reliability Analysis of Systems Using Level (λ, 1) Interval-valued Fuzzy Sets Considering the Widths
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초록
퍼지시스템의 신뢰도를 평가하는데 사용하는 퍼지집합이론에는 다양한 형태의 퍼지집합들이 있다. 퍼지집합에서는 소속값 를 실수로 표현한다. ∈ . 그러나 이 소속값이 불확실한 경우 실수로 표현하는 것이 어렵게 된다. 이러한 문제를 해결하기위해 제안된 방법이 구간값 퍼지 집합이다. 구간값 퍼지집합에서는 소속값을 구간 [, ]로 표현한다. 는 최소 소속값이고 는 최대 소속값이다. [, ] ⊆ . 0 ≤ ≤ ≤ 1. 그러나 최소 소속값과 최대 소속값이 정해지면 그 값은 상수로 고정이 된다. 그러므로 소속값을 조정하는 것이 어려워진다. 이러한 문제를 극복한 방법이 수준 (λ, 1) 구간값 퍼지집합이 제안되었다. 수준 (λ, 1) 구간값 퍼지집합에서는 λ를 이용하여 최소 소속값의 크기를 조정하는 것이 가능하게 된다. 본 논문에서는 수준 (λ, 1) 구간값 퍼지집합과 수준 (λ, 1) 구간값 퍼지집합의 소속값인 구간의 너비를 이용하여 시스템의 신뢰도를 평가하는 방법을 제안하였다. 제안한 방법은 수준 (λ, 1) 구간값 퍼지집합과 수준 (λ, 1) 구간값 퍼지집합의 소속값인 구간의 너비를 이용하므로 기존의 방법보다 더 엄밀하게 시스템의 신뢰도를 평가하는 것이 가능하게 된다.
Abstract
In the fuzzy set theory there are various types of the fuzzy sets to deal with the reliability of systems. In the fuzzy sets the degree of membership is represented by real number. ∈ . Sometimes the membership degree of the fuzzy sets can not be represented by real number because the degree of membership itself may has the uncertainty. To overcome this problem the interval valued fuzzy sets are proposed. In the interval valued fuzzy sets the degree of membership is represented by interval [, ]. is the smallest degree of memebership and is the greatest degree of membership. [, ] ⊆ . 0 ≤ ≤ ≤ 1. Once the degrees of membership of the interval valued fuzzy serts are assigned as some reals and then these numbers can not be resized. In order to resolve the this demerit the level (λ, 1) interval valued fuzzy sets are introduced. In the level (λ, 1) interval valued fuzzy sets the smallest degree of membership can be resize using the λ. In this paper we propose the way to evaluate the reliability of systems based on the level (λ, 1) interval valued fuzzy sets and its widths. The proposed method may be used to analyze the reliability of systems which have the concept of the level (λ, 1) interval valued fuzzy sets and may be able to evaluate the relaibility more accuracy than the interval valued fuzzy sets because of using the the level (λ, 1) interval valued fuzzy sets and its widths.
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