퍼지수 직관적 판단행렬

Abstract

본 논문에서는 직관적 퍼지집합(intuitionistic fuzzy set)과 구간치 직관적 퍼지집합(interval-valued intuitionistic fuzzy set)을 소개하고 이들의 확장된 개념인 퍼지수 직관적 퍼지집합(fuzzy number intuitionistic fuzzy set)을 정의 하였다. 또한 그들의 연산법칙과 스코어함수, 정확도 함수를 제시하고, 선호도 정보를 모으기 위한 집합연산자(FIFA, FIFWA, FIFOWA, FIFHA)를 소개하였다. 이를 기초로, 퍼지수 직관적 판단행렬(fuzzy number intuitionistic judgment matrix)과 그것의 스코어행렬(score matrix), 정확도행렬(accuracy matrix)과 같은 새로운 개념을 정의하고 그들의 기본적 성질을 밝힌다. 또한, 퍼지수 직관적 판단행렬을 이용하여 의사결정 문제 해결에의 응용과정과 그 예를 제공하였다.

In this thesis, we have investigated the aggregation of fuzzy number intuitionistic information, and developed some aggregation operators, such as, the ordered weighted aggregation operator and the hybrid aggregation operator of FNIFNs. we have defined a new judgment matrix called the fuzzy number intuitionistic judgment matrix and studied some of its desirable properties, and then defined the concepts of the consistent fuzzy number intuitionistic judgment matrix, and the score matrix, and accuracy matrix of the fuzzy number intuitionistic judgment matrix, and so on. we have shown that the score matrix and accuracy matrix are the antisymmetric matrix and symmetric matrix respectively, and discussed the relationships among fuzzy number intuitionistic judgment matrix, intuitionistic judgment matrix, and complement judgment matrix. Furthermore, on the basis of the arithmetic aggregation operator and hybrid aggregation operator, we have proposed an approach for solving the group decision-making problems where the decision makers provide their preferences over alternatives in the form of fuzzy number intuitionistic judgment matrices. In the future, the developed aggregation operators of FNIFNs can be applied to the fields of pattern recognition, artificial intelligence, data mining, fuzzy logic, and so on.