基于区间直觉模糊的多属性决策模型及应用研究  

MULTI-ATTRIBUTE DECISION-MAKING MODEL BASED ON INTERVAL-VALUED INTUITIONISTIC FUZZY AND ITS APPLICATION

作　　者：谢小军 马虹 薛申芳 骆旗 XIE Xiaojun;MA Hong;XUE Shenfang;LUO Qi(School of General Education,Guangzhou College of Technology and Business,Guangzhou,Guangdong 510850,China;School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou,Guangdong 510521,China)

机构地区：[1]广州工商学院通识教育学院,广东广州5108501 [2]广东金融学院金融数学与统计学院,广东广州510521

出　　处：《井冈山大学学报(自然科学版)》2025年第1期14-21,共8页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(61572016);广东省2022年度普通高校重点科研平台和项目(2022ZDZX1037)。

摘　　要：在多属性决策问题中专家的评价信息很难用精确值来表示,而基于区间直觉模糊的多属性决策模型越来越受到研究者的关注。在区间直觉模糊的多属性决策模型中,度量两个区间直觉模糊数向量的相似度和确定评价属性权重是其中重要的步骤。本研究的主要贡献包括:(1)针对经典投影测度公式的缺陷,提出了一种新的广义标准化投影测度公式,该公式能够更加准确地测度两个区间直觉模糊数向量的相似度;(2)针对评价信息为区间直觉模糊数,利用投影测度公式拓展TOPSIS方法,构建了新的多属性决策模型;(3)针对评价属性权重未知的情况,以各备选方案的评价指标具有较好的区分度为思想构建了优化模型,从而提出了一种确定评价属性权重的客观方法。最后,将本研究模型应用于实际案例中,通过对比分析,验证了模型的可行性和有效性。It has become difficult to represent expert evaluation information in multi-attribute decision-making problems with precise values.As a result,interval intuitionistic fuzzy multi-attribute decision models have garnered growing attention from researchers.In these models,two critical steps are measuring the similarity between two interval intuitionistic fuzzy number vectors and determining the attribute weights.The main contributions of this study include:(1) In response to the limitations of the classical projection measure formula,a new generalized normalized projection measure formula is proposed,which provides a more accurate assessment of the similarity between two interval intuitionistic fuzzy number vectors;(2) Based on interval intuitionistic fuzzy evaluation information,the projection measure formula presented in this paper is used to extend the TOPSIS method,thereby constructing a new multi-attribute decision model;(3) In cases where the evaluation attribute weights are unknown,an optimization model is developed based on the principle of maximizing the differentiation of evaluation indicators across alternatives,resulting in an objective method for determining the attribute weights.Finally,the proposed model is applied to a real-world case,and through comparative analysis,its feasibility and effectiveness are validated.

关 键 词：多属性决策模型 标准化投影 区间直觉模糊数 TOPSIS方法 属性权重 

分 类 号：O159[理学—数学] C934[理学—基础数学]