论文标题
毕达哥拉斯的圆形模糊集和多标准决策的应用
Circular Pythagorean fuzzy sets and applications to multi-criteria decision making
论文作者
论文摘要
在本文中，我们介绍了圆形毕达哥拉斯模糊集（值）（c-pfs（v））作为对Atannassov和Pythagorean Fuzzy Fuzzy Sets（PFSS）提出的两个圆形直觉模糊集（C-IFS）的新概括。一个圆形的毕达哥拉斯模糊集由代表会员学位和非会员学位的圆圈表示，其中心由非负实数$μ$和$ν$组成，条件$μ^2+μ^2+ν^2 \ leq 1 $。 C-PFS由于其结构允许用特定中心和半径的圆的点对信息进行建模，因此更正确地对不确定信息的模糊进行了建模。因此，C-PF使决策者可以评估更大，更灵活的区域中的对象，从而可以做出更敏感的决策。在定义了C-PF的概念之后，我们定义了C-PFS之间的一些基本设置操作，并通过一般$ t $ - 纳米和$ t $ - conorms提出了C-PFV之间的一些代数操作。通过利用这些代数操作，我们引入了一些加权聚合操作员来将C-PFV代表的输入值转换为单个输出值。然后，为了确定C-PFV之间的相似性程度，我们根据半径定义了余弦相似性度量。此外，我们开发了一种将毕达哥拉斯模糊值集合转换为PFS的方法。最后，给出了一种方法来解决圆角毕达哥拉斯模糊环境中的多准则决策问题，并实践了提出的方法，即从文献中选择最佳光伏细胞的问题。我们还研究了所提出的方法的比较分析和时间复杂性。
In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the non-membership degree and whose center consists of non-negative real numbers $μ$ and $ν$ with the condition $μ^2+ν^2\leq 1$. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain center and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general $t$-norms and $t$-conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method.
