Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

Journal of Systems Science and Information Pub Date : 2020-12-01 DOI:10.21078/JSSI-2020-524-25

Qian Yu, Jun Cao, Ling Tan, Yubing Zhai, Jiongyang Liu

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Abstract

Abstract In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant trapezoid fuzzy information. Firstly, inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers, the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed. Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed, such as the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator, the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator, the hesitant trapezoid fuzzy Hamacher Choquet average (HTrFHCA), the hesitant trapezoid fuzzy Hamacher Choquet geometric (HTrFHCG), etc. Furthermore, an approach based on the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator and the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator is proposed for MADM problems under hesitant trapezoid fuzzy environment. Finally, a numerical example for supplier selection is given to illustrate the application of the proposed approach.

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犹豫梯形模糊Hamacher聚合算子及其在多属性决策中的应用

摘要研究了属性值采用犹豫梯形模糊信息形式的多属性决策问题。首先，受犹豫模糊集和梯形模糊数思想的启发，提出了犹豫梯形模糊集的定义和犹豫梯形模糊元的一些运算规律;在此基础上，提出了基于Hamacher运算的犹豫梯形模糊聚集算子，如犹豫梯形模糊Hamacher加权平均算子(HTrFHWA)、犹豫梯形模糊Hamacher加权几何算子(HTrFHWG)、犹豫梯形模糊Hamacher Choquet平均算子(HTrFHCA)、犹豫梯形模糊Hamacher Choquet几何算子(HTrFHCG)等。在此基础上，提出了一种基于犹豫梯形模糊Hamacher加权平均算子(HTrFHWA)和犹豫梯形模糊Hamacher加权几何算子(HTrFHWG)的求解犹豫不决梯形模糊环境下MADM问题的方法。最后，给出了一个供应商选择的数值例子来说明该方法的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Systems Science and Information

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