Pythagorean Triangular Fuzzy Linguistic Hamacher Aggregation Operators and Their Application

doi:10.12005/orms.2018.0065

Abstract

Abstract: Based on the Pythagorean fuzzy set and Hamacher operator, the Pythagorean triangular fuzzy linguistic Hamacher aggregation operators are studied. Firstly, the definition, the operational laws, score function and accuracy function of the Pythagorean triangular fuzzy linguistic set are proposed. Then, a series of Pythagorean triangular fuzzy linguistic Hamacher aggregation operators are developed, such as the Pythagorean triangular fuzzy linguistic Hamacher weighted average (PTrFLHWA) operator and the Pythagorean triangular fuzzy linguistic Hamacher geometric (PTrFLHWG) operator. Moreover, some properties of these operators are discussed in detail. Afterwards, two new approaches to Pythagorean triangular fuzzy linguistic multi-attribute group decision making are presented based on the proposed operators. Finally, a practical example is given to illustrate the effectiveness of the proposed approaches.

Key words: pythagorean triangular fuzzy linguistic variable, multi-attribute group decision making, hamacher operator, aggregation operator

摘要： 在Pythagorean模糊集和Hamacher集结算子基础上,研究了Pythagorean三角模糊语言环境下的Hamacher集成算子问题。首先给出了Pythagorean三角模糊语言的定义、运算规则、得分函数、精确函数;其次,介绍了一系列关于Pythagorean三角模糊语言Hamacher集结算子,比如Pythagorean三角模糊语言Hamacher加权平均算子(PTrFLHWA)、Pythagorean三角模糊语言Hamacher加权几何平均算子(PTrFLHWG)等,并研究其具有的性质;之后,提出了两种决策方法来解决Pythagorean三角模糊语言信息环境下的多属性群决策问题;最后,用示例验证所给方法的有效性。

关键词: Pythagorean三角模糊语言变量, 多属性群决策, Hamacher算子, 集成算子

CLC Number:

C934

DU Yu-qin, HOU Fu-jun, ZHAI Yu-bing, YU-qian. Pythagorean Triangular Fuzzy Linguistic Hamacher Aggregation Operators and Their Application[J]. Operations Research and Management Science, 2018, 27(3): 104-112.

杜玉琴, 侯福均, 翟玉冰, 于倩. Pythagorean三角模糊语言Hamacher集结算子及其应用[J]. 运筹与管理, 2018, 27(3): 104-112.

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