毕达哥拉斯模糊软集的相似性测度及其应用

Similarity Measure of Pythagorean Fuzzy Soft Sets and Its Applications

直觉模糊软集不能处理隶属度与非隶属度之和大于1的情况,且现有的直觉模糊软集的相似性测度只考虑了隶属度与非隶属度,忽视了犹豫度。针对以上问题,本文提出了一种基于隶属度、非隶属度以及犹豫度三个参数的毕达哥拉斯模糊软集的相似性测度和加权相似性测度。在为加权相似性测度的权重取值时,本文基于现有文献中直觉模糊熵存在的缺陷建立一种改进的直觉模糊熵,利用熵权法计算权重。分别讨论两相似性测度公式的性质,最后将两相似性侧度公式应用在建筑材料的模式识别问题中。

Intuitionistic fuzzy soft set can not deal with the case where the sum of membership degree and non-membership degree is greater than 1, and the existing similarity measure of intuitionistic fuzzy soft set only considers membership degree and non-membership degree, ignoring the degree of hesitation. In order to solve the above problems,this paper proposes a similarity measure and weighted similarity measure of Pythagorean fuzzy soft set based on membership degree, non-membership degree and hesitation degree. When the weight of weighted similarity measure is taken, an improved intuitionistic fuzzy entropy is established based on the defects of intuitionistic fuzzy entropy in the existing literature, and the weight is calculated by entropy weight method. In addition, the properties of the two similarity measure formulas are discussed respectively. Finally, the two similarity measure formulas are applied to the pattern recognition of building materials.