一种新的直觉模糊集距离及其在决策中的应用  

New distance between intuitionistic fuzzy sets and its applications in decision-making

作　　者：许昌林[1,2,3] 沈菊红 Xu Changlin;Shen Juhong(Key Laboratory of Intelligent Information&Big Data Processing of Ningxia Province,North Minzu University,Yinchuan 750021,China;School of Mathematics&Information Sciences,North Minzu University,Yinchuan 750021,China;Health Big Data Research Institute,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学宁夏智能信息与大数据处理重点实验室,银川750021 [2]北方民族大学数学与信息科学学院,银川750021 [3]北方民族大学健康大数据研究所,银川750021

出　　处：《计算机应用研究》2020年第12期3627-3634,共8页Application Research of Computers

基　　金：宁夏高等学校科学研究资助项目(NGY2020067);宁夏自然科学基金资助项目(2018AAC03253,2020AAC03217);国家自然科学基金资助项目(61662001);北方民族大学重大专项资助项目(ZDZX201801,ZDZX201804)。

摘　　要：首先针对直觉模糊集距离中是否包含直觉模糊集通过隶属度、非隶属度以及犹豫度这三种信息,以及直觉模糊集距离是否满足相应距离度量的条件对其进行了详细分析,发现现有方法都是将犹豫度直接引入到直觉模糊集距离中,从而产生不一致性。鉴于此,定义了一种新的直觉模糊集距离度量方法,不仅考虑隶属度和非隶属度信息,同时还考虑犹豫度对隶属度和非隶属度的分配,从而间接地将犹豫度也引入到直觉模糊集距离中。其次,证明了所提距离度量满足距离度量条件,并结合实例将其与现有距离度量方法进行比较分析,说明了新方法的合理性。最后,将所提出方法应用于多准则模糊决策中,进一步说明了新方法的有效性和可行性。This paper firstly analyzed the drawbacks of the existing distance measures between intuitionistic fuzzy sets in detail,which was based on whether the distance measures between intuitionistic fuzzy sets contained the membership degree,non-membership degree and hesitation degree,and whether the distance measures between intuitionistic fuzzy sets satisfied the conditions of the distance metric.In view of the fact,it directly introduced the hesitation degree into the distances of intui-tionistic fuzzy sets in the existing distance measures,which led to inconsistency.Then on the base of these,this paper proposed a new distance measure between intuitionistic fuzzy sets.The new method not only considered the membership degree information and the non-membership degree information,but also considered the assignments of the hesitation degree to membership degree and non-membership degree.Thereby,it indirectly introduced the degree of hesitation into the new distance.Secondly,it analyzed and proved some properties of the proposed distance,and compared with the existing methods to illustrate its reasonability based on some practical examples.Finally,it further illustrated the effectiveness and feasibility of the proposed method by the multi-criteria fuzzy decision-making.

关 键 词：直觉模糊集 距离 相似度量 多准则模糊决策 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]