毕达哥拉斯不确定语言Maclaurin对称集成算子及其在多属性决策中的应用

Pythagorean Uncertain Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multi-attribute Decision Making

毕达哥拉斯不确定语言变量是直觉不确定语言变量的拓展和一般化.针对毕达哥拉斯不确定语言变量的集成问题,首先结合语言刻度函数,提出新的毕达哥拉斯不确定语言变量运算法则和排序方法,克服已有运算存在的缺少封闭性和灵活性的不足.进而,提出了捕获多元关联关系的毕达哥拉斯不确定语言Maclaurin对称集成算子(PULMSM)及其加权形式(PULWMSM),并探讨其优良性质和特例.最后,提出一种基于PULWMSM的毕达哥拉斯不确定语言多属性决策方法,并通过实例来分析其合理性和有效性.

Pythagorean uncertain linguistic variables are the extension and generalization of intuitionistic uncertain linguistic variables.In order to aggregate Pythagorean uncertain linguistic variables,some new operational laws and comparison method of the Pythagorean uncertain linguistic variables are proposed by combining with linguistic scale function,which overcomes the shortcomings of closeness and flexibility in existing operations.Furthermore,the Pythagorean uncertain linguistic Maclaurin symmetric mean operator (PULMSM)and its weighted form (PULWMSM)are proposed to aggregate Pythagorean uncertain linguistic variables,which can model the interrelationship among multi-inputs.Meanwhile,some of desirable properties and special cases are discussed.Finally,a Pythagorean uncertain linguistic multi-attribute decision making method is proposed based on the proposed PULMSM operator,then an illustrative example is conducted to show the rationality and effectiveness.