基于TOPSIS的语言真值直觉模糊多属性决策

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Title:

Linguistic truth-valued intuitionistic fuzzy multi-attribute decision making based on TOPSIS

作者:

徐莹莹¹, 邹丽¹, 黄志鑫², 潘畅¹

1. 辽宁师范大学 计算机与信息技术学院, 辽宁 大连 116081;
2. 辽宁师范大学 数学学院, 辽宁 大连 116081

Author(s):

XU Yingying¹, ZOU Li¹, HUANG Zhixin², PAN Chang¹

1. School of Computer and Information Technology, Liaoning Normal University, Dalian 116081, China;
2. School of Mathematics, Liaoning Normal University, Dalian 116081, China

关键词:

TOPSIS; 语言真值直觉模糊对; 归一化距离; 理想点; 多属性决策

Keywords:

TOPSIS; linguistic truth-valued intuitionistic fuzzy pairs; normalized distance; ideal point; multi-attribute decision making

分类号:

TP181

DOI:

10.11992/tis.201608008

摘要:

针对具有模糊语言值信息的多属性决策问题，结合传统的TOPSIS方法，提出了基于TOPSIS的语言真值直觉模糊多属性决策方法。在语言真值直觉模糊代数的基础上，用语言真值直觉模糊对来表达既有可比的又有不可比的模糊语言值信息，给出了语言真值直觉模糊对之间的归一化距离算法，并讨论了其相关性质。提出了语言真值直觉模糊正、负理想点，通过计算各方案属性值与正、负理想点之间的距离，得到各方案与理想点之间的相对贴近度，并根据相对贴近度的排序结果得到最优方案。实例说明该决策方法的合理性和有效性。

Abstract:

For multi-attribute decision making problems with fuzzy linguistic-valued information, in this paper, we propose a linguistic truth-valued intuitionistic fuzzy multi-attribute decision making approach based on the technique for order performance by similarity to ideal solution (TOPSIS), in combination with the traditional TOPSIS approach. On the basis of linguistic truth-valued intuitionistic fuzzy algebra, in our approach, we used linguistic truth-valued intuitionistic fuzzy pairs to express fuzzy linguistic-valued information that is both comparable and incomparable. We define the normalized distance algorithm for linguistic truth-valued intuitionistic fuzzy pairs and discuss its related properties. We propose linguistic truth-valued intuitionistic fuzzy positive and negative ideal points by calculating the distances between the attribute values of every scheme with positive and negative ideal points to obtain their relative degree of closeness. From the ranking result of the relative degree of closeness, we can determine the best scheme. We give an example to illustrate the reasonability and effectiveness of our proposed decision-making approach.