基于Pythagorean模糊语言集多属性群决策方法

计算机工程与应用 ›› 2016, Vol. 52 ›› Issue (23): 50-54.

基于Pythagorean模糊语言集多属性群决策方法

彭新东，杨勇

西北师范大学计算机科学与工程学院，兰州 730070

出版日期:2016-12-01 发布日期:2016-12-20

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

PENG Xindong, YANG Yong

College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China

Online:2016-12-01 Published:2016-12-20

摘要/Abstract

摘要： 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。

关键词: Pythagorean模糊语言集, Pythagorean模糊语言数, 组合权重, 逼近理想解排序法（TOPSIS）

Abstract: 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.

Key words: Pythagorean fuzzy linguistic set, Pythagorean fuzzy linguistic number, combined weight, Technique for Order Preference Similarity to Ideal Solution（TOPSIS）

彭新东，杨勇. 基于Pythagorean模糊语言集多属性群决策方法[J]. 计算机工程与应用, 2016, 52(23): 50-54.

PENG Xindong, YANG Yong. Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set[J]. Computer Engineering and Applications, 2016, 52(23): 50-54.

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