基于投影法和夹角度量法的改进TOPSIS

李美娟,袁宁,陈磊

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (9) : 1614-1627.

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PDF(701 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (9) : 1614-1627. DOI: 10.12341/jssms13968
论文

基于投影法和夹角度量法的改进TOPSIS

    李美娟,袁宁,陈磊
作者信息 +

Improved TOPSIS Based on Projection Method and Angle Measure Evaluation Method

    LI Meijuan, YUAN Ning ,CHEN Lei
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文章历史 +

摘要

针对多属性决策评价问题,为了克服传统 理想解法欧式距离的缺陷,提出一种基于投影法和 夹角度量法的改进TOPSIS方法.该方法以理想解法为 基础模型,由灰色关联度法确定各评价指标的权重,然 后通过投影法和夹角度量法计算各待评价方案到理想 解和虚拟最劣解的正负投影距离和正负夹角,最后将 两者的评价值进行有机结合,构造一种新的相对贴近度------投影夹角系 数来实现对各待评价方案的综合评价.该方法综合了灰色关联度法、投 影法、夹角度量法三种方法的优势,构造了一种更全面的综合评价方法,最后文章将该方法与TOPSIS 法、夹角度量法、正交投影法进行了分析对比,通过实例证明了该 方法的可行性与有效性。

Abstract

In this paper, we present a new TOPSIS method based on projection method and angle measure evaluation method for the purpose of overcoming the defects caused by the traditional TOPSIS Euclidean distance. This method is based on TOPSIS, and the weight of each evaluation index is determined by grey correlation degree. Meanwhile, the relative projection distance and angle of each evaluation scheme to the ideal solution and the virtual worst solution are calculated by projection method and angle measure evaluation method, and a new relative similarity degree is established by combining projection method and angle measure evaluation method. At the end, this method is compared with TOPSIS method, angle measure evaluation method and vertical projection method and the feasibility and effectiveness of this method are explained by example.

关键词

灰色关联度法 / 投影法 / 夹角度量法 / 理想解法.

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李美娟 , 袁宁 , 陈磊. 基于投影法和夹角度量法的改进TOPSIS. 系统科学与数学, 2020, 40(9): 1614-1627. https://doi.org/10.12341/jssms13968
LI Meijuan , YUAN Ning , CHEN Lei. Improved TOPSIS Based on Projection Method and Angle Measure Evaluation Method. Journal of Systems Science and Mathematical Sciences, 2020, 40(9): 1614-1627 https://doi.org/10.12341/jssms13968
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