直觉模糊集的减法和除法运算的新定义  

A New Definition of Subtraction and Division Operations for Intuitionistic Fuzzy Sets

作　　者：马虹 谢小军 

机构地区：[1]广东金融学院金融数学与统计学院,广东 广州 [2]广州工商学院通识教育学院,广东 广州

出　　处：《运筹与模糊学》2023年第6期7789-7796,共8页Operations Research and Fuzziology

摘　　要：模糊集合的概念自提出以来,其扩展形式不断得到丰富,其中最为经典的是直觉模糊集和区间直觉模糊集两个概念,后续直觉模糊集和区间直觉模糊集理论被广泛应用于处理决策信息不确定的问题。我们对直觉模糊集的关系和基本运算进行了梳理,发现现有的研究成果中没有定义直觉模糊集的减法和除法运算。因此,我们通过基于直觉模糊集已有的基本运算规则定义了减法和除法两种新运算,证明了基于直觉模糊数的减法和除法是封闭的,并进一步将直觉模糊集上的基本运算规则推广到区间直觉模糊集和区间直觉模糊数上,证明了基于区间直觉模糊数的和、差、积、商运算是封闭的。本文的最重要的贡献是使得直觉模糊集和区间直觉模糊集有了完整的四则运算,从而丰富了其理论基础。Since the concept of fuzzy sets was proposed, its extended form has been continuously enriched, among which the most classical ones are the concepts of intuitionistic fuzzy sets and interval intuitionistic fuzzy sets, and the subsequent theories of intuitionistic fuzzy sets and interval intuitionistic fuzzy sets have been widely used to deal with the problems of uncertainty of decision-making information. We have sorted out the relations and basic operations of intuitionistic fuzzy sets and found that the subtraction and division operations of intuitionistic fuzzy sets are not defined in the existing research results. Therefore, we prove that subtraction and division based on intuitionistic fuzzy numbers are closed by defining two new operations, subtraction and divi-sion, based on the existing basic operation rules of intuitionistic fuzzy sets, and further extend the basic operation rules on intuitionistic fuzzy sets to interval intuitionistic fuzzy sets and in-terval intuitionistic fuzzy numbers, and prove that the sum, difference, product, and quotient operations based on interval intuitionistic fuzzy numbers are closed. The most important contribution of this paper is to make intuitionistic fuzzy sets and interval intuitionistic fuzzy sets have complete four-rule operations, which enriches their theoretical foundation.

关 键 词：模糊数学 直觉模糊集 区间直觉模糊集 运算规则 

分 类 号：G62[文化科学—教育学]