毕达哥拉斯模糊还原性BM算子及其决策应用

还原性是信息集成算子的一个重要性质.针对毕达哥拉斯模糊加权Bonferroni平均(BM)算子不具有还原性的情况,提出了具有还原性的毕达哥拉斯模糊BM算子,并研究了其决策应用.首先,定义了毕达哥拉斯模糊还原性加权BM算子(PFRWBM)和广义毕达哥拉斯模糊还原性加权BM算子(GPFRWBM),推导出它们的计算公式,证明了它们的性质.随后,定义了毕达哥拉斯模糊还原性加权BGM算子(PFRWGBM)和广义毕达哥拉斯模糊还原性BGM算子(GPFRWBGM),给出它们的计算公式,讨论了它们的性质.最后,提出了基于毕达哥拉斯模糊还原性加权BM算子的多属性决策方法,并通过实例和方法对比说明了所提方法的可行性.

Pythagorean fuzzy BM operators with reducibility and applications in decision making

Reducibility is an important property of aggregation operator. Aiming at Pythagorean fuzzy weighted Bonferroni mean (BM) operator without reducibility in related references, the Pythagorean fuzzy reducible weighted BM operators and their applications in decision making are discussed. Pythagorean fuzzy reducible weighted BM operator (PFRWBM) is defined, and the mathematical expression of this operator is obtained by derivation and some properties of this operator are discussed. Almost immediately generalized Pythagorean fuzzy reducible weighted BM operator (GPFRWBM) is proposed, and its mathematical expression is given and some properties are also discussed. Then, Pythagorean fuzzy reducible weighted BGM operator (PFRWBGM) and generalized Pythagorean fuzzy reducible weighted BGM operator (GPFRWBGM) are also defined, and their mathematical expression are given and some properties of these operators are discussed. Finally, an approach to multiple attribute decision making based on PFRWBM operators is proposed, and a practical example is given to illustrate our results.