基于Pythagorean模糊语言集多属性群决策方法

为了解决直觉语言集不能够处理隶属于与非隶属于语言值的程度之和大于1的情况，提出了Pythagorean模糊语言集。针对Pythagorean模糊语言信息的集成问题，定义了Pythagorean模糊语言数的运算法则及其得分函数、精确函数，提出了Pythagorean模糊语言加权平均（PFLWA）算子、Pythagorean模糊语言有序加权平均（PFLOWA）算子、Pythagorean模糊语言混合平均（PFLHA）算子，并讨论了相应的性质。然后基于组合权重的PFLWA算子与拓展的TOPSIS，提出了两种多属性群决策方法。最后通过实例验证了该方法的有效性。

Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set

In order to solve the problem that intuitionistic linguistic set can’t deal with the situation that the sum of membership degree and non-membership degree belonging to linguistic value is bigger than 1, and Pythagorean fuzzy linguistic set is proposed. For the Pythagorean fuzzy linguistic information aggregating problems, some operational laws, score function, and accuracy function of Pythagorean Fuzzy Linguistic Numbers（PFLNs） are defined. Based on the operational laws, the Pythagorean Fuzzy Linguistic Weighted Averaging（PFLWA） operator, Pythagorean Fuzzy Linguistic Ordered Weighted Averaging（PFLOWA） operator, and Pythagorean Fuzzy Linguistic Hybrid Averaging（PFLHA） operator are proposed, and some desirable properties are discussed in detail. Then, based on PFLWA operator and extension of TOPSIS with combined weight, two approaches for solving multiple attribute group decision making are explored. Finally, an illustrative example shows the effectiveness of the methods.