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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (3): 389-400.doi: 10.3969/j.issn.1005-3085.2022.03.004

• • 上一篇    下一篇

基于直觉模糊张量的决策方法及其应用

邓胜岳1,   谭金桃1,   宋玉琴1,   申  静2   

  1. 1. 湖南工业大学理学院，株洲  412007 
    2. 湖南工业大学经济与贸易学院，株洲 412007
  • 出版日期:2022-06-15 发布日期:2022-08-15
  • 通讯作者: 申 静 E-mail: shenjing41@aliyun.com
  • 基金资助:
    国家自然科学基金 (11971413; 11747104; 71801090); 湖南省自然科学基金 (2020JJ4264; 2020JJ4265); 湖南省教育厅科学研究项目优秀青年项目 (20B180).

Decision Making Method Based on Intuitionistic Fuzzy Tensor and Its Application

DENG Shengyue1,  TAN Jintao1,  SONG Yuqin1,  SHEN Jing2   

  1. 1. School of Science, Hunan University of Technology, Zhuzhou 412007
    2. College of Economics and Trade, Hunan University of Technology, Zhuzhou 412007
  • Online:2022-06-15 Published:2022-08-15
  • Contact: J. Shen. E-mail address: shenjing41@aliyun.com
  • Supported by:
    The National Natural Science Foundation of China (11971413; 11747104; 71801090); the Natural Science Foundation of Hunan Province (2020JJ4264; 2020JJ4265); the Outstanding Youth Project of Hunan Provincial Education Department (20B180).

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摘要：

对具有高维数据特征的直觉模糊决策问题进行了研究，定义了直觉模糊张量的一般形式和运算法则；建立了基于直觉模糊张量的广义直觉模糊加权平均算子，探索了广义直觉模糊加权平均算子的基本性质；证明了广义直觉模糊加权平均算子是直觉模糊加权平均算子的一般形式。提出了基于广义直觉模糊加权平均算子的决策方法，通过算例验证了该方法能够有效解决具有高维数据特征的直觉模糊决策问题。

关键词: 直觉模糊张量, 广义直觉模糊加权平均算子, 动态多属性决策, 群决策

Abstract:

The intuitionistic fuzzy decision-making problem with high-dimensional data is stu-died in this paper. The general form and operational laws of the intuitionistic fuzzy tensor are defined, the generalized intuitionistic fuzzy weighted averaging (GIFWA) operator based on the intuitionistic fuzzy tensor is subsequently established. By exploring the basic properties of the GIFWA operator, it is proved that the GIFWA operator is a general form of the intuition-istic fuzzy weighted average operator. A novel decision-making method based on the GIFWA operator is presented to solve the intuitionistic fuzzy decision problems with high-dimensional data. One typical example is also provided to demonstrate the efficiency and applicability of our proposed method.

Key words: intuitionistic fuzzy tensor, generalized intuitionistic fuzzy weighted averaging operator, dynamic multiple attribute decision making, group decision making

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