基于空间信息表征的勾股模糊集空间距离测度

Spatial distance measure of Pythagorean fuzzy sets based on spatial information representation

勾股模糊集拓展了直觉模糊集的信息表征内容,具有体现更大信息空间的优势,构建勾股模糊集的距离测度是实施勾股模糊型决策的核心环节。本文首先分析了现有4种勾股模糊集距离测度的缺陷,构建了融合隶属度、非隶属度、犹豫度和自信度的勾股模糊集空间信息表征模型,进而提出了基于勾股模糊集空间质心的距离测度。其次,拓展了距离测度的具体特性,比较了所提距离测度模型在体现犹豫度和解决反直觉情形方面的优势。最后,模式识别和医疗诊断等应用研究证明了所提距离测度的准确性和优越性。

Pythagorean fuzzy set expands the information representation content of intuitionistic fuzzy sets and has the advantage of reflecting larger information space.Constructing the distance measure of Pythagorean fuzzy sets is the core link of implementing Pythagorean fuzzy decision-making.Firstly,this paper deeply analyzes the defects of the existing four distance measures of Pythagorean fuzzy sets,establishes a spatial information representation model of Pythagorean fuzzy sets integrating the membership degree and nonmembership degree,hesitation degree and strength of commitment,and then puts forward a novel distance measure based on the spatial centroid of Pythagorean fuzzy sets.Secondly,the specific properties of the proposed distance measure are extended,and the advantages of this distance measure model in reflecting hesitation and solving counterintuitive situations are proven and compared.Finally,the application research of pattern recognition and medical diagnosis verifies the accuracy and superiority of this distance measure between Pythagorean fuzzy sets.