引用本文:范建平,闫彦,吴美琴.基于三角Pythagorean模糊集的多准则决策方法[J].控制与决策,2019,34(8):1601-1608
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基于三角Pythagorean模糊集的多准则决策方法
范建平,闫彦, 吴美琴
(山西大学经济与管理学院,太原030006)
摘要:
Pythagorean模糊集在直觉模糊集的基础上扩大了适用范围,三角模糊数在决策过程中可以保留决策者较多的不确定信息.鉴于此,首先提出三角Pythagorean模糊集的定义及其欧氏距离表示;然后定义三角Pythagorean模糊加权平均(TPFWA)算子、广义三角Pythagorean模糊加权平均(GTPFWA)算子、三角Pythagorean模糊加权几何(TPFWG)算子和广义三角Pythagorean模糊加权几何(GTPFWG)算子,并对算子所满足的幂等性、有界性和单调性予以证明;最后通过一个医药代表选择的多准则决策问题和灵敏度分析验证所提出算子的合理性和有效性.
关键词:  三角Pythagorean模糊集  欧氏距离  三角Pythagorean模糊集结算子  广义三角Pythagorean模糊集结算子  多准则决策问题
DOI:10.13195/j.kzyjc.2017.1779
分类号:TP273
基金项目:
Triangular Pythagorean fuzzy set and its application to multicriteria decision making
FAN Jian-ping,YAN Yan,WU Mei-qin
(School of Economics and Management,Shanxi University,Taiyuan030006,China)
Abstract:
Pythagorean fuzzy sets expand the range of application based on intuitionistic fuzzy sets, triangular fuzzy number reserves more uncertain information in the decision making process. Firstly, a triangular Pythagorean fuzzy set and Euclidean distance are defined. Then, triangular Pythagorean fuzzy weighted averaging(TPFWA), generalized triangular Pythagorean fuzzy weighted averaging(GTPFWA), triangular Pythagorean fuzzy weighted geometric(TPFWG) and generalized triangular Pythagorean fuzzy weighted geometric(GTPFWG) operators are defined, and correlative idempotency, boundedness and monotonity are proved. Finally the reasonableness and validity are verified by a multicriteria decision making about medical representative selection and sensitivity analysis.
Key words:  triangular Pythagorean fuzzy set  Euclidean distance  triangular Pythagorean fuzzy weighted operators  generalized triangular Pythagorean fuzzy weighted operators  multicriteria decision making

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