综合理想点和反理想点距离的多标准方法

Symmetry Pub Date : 2024-08-11 DOI:10.3390/sym16081025
Ewa Roszkowska, Marzena Filipowicz-Chomko
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引用次数: 0

摘要

基于参考点和与参考点距离的多标准决策方法,对于评估多个标准的备选方案至关重要。这些方法提供了相对于指定参考点对备选方案进行比较和排序的结构化方法。本文的主要目的是介绍 "整合理想点与反理想点距离的多标准方法"(MIDIA),该方法通过一个加权系统,在根据备选方案与理想点和反理想点的距离对其进行评估时,可考虑平衡性和不对称性。作为一种多标准算法,MIDIA 易于使用,反映了人类基于基本概念(与理想方案和反理想方案的比较)评估对象的自然倾向,这些基本概念在日常经验中耳熟能详,并能从行为学角度提供有价值的见解。此外,所提出的方法可视为赫尔维格方法的延伸,旨在促进基于两个参考点(理想点和反理想点)对备选方案进行排序,测量备选方案与理想点之间的距离以及理想点与反理想点之间的距离。MIDIA 方法融合了 TOPSIS 和 VIKOR 的元素,既有 TOPSIS 的结构,又有 VIKOR 的折中观点,通过关注理想点和反理想点之间的距离,为多标准决策提供了一种平衡的方法。本文举例说明了在决策者对理想点和反理想点在备选方案排序中的重要性具有不对称偏好的情况下,所建议工具的可用性。此外,还将 MIDIA 方法应用于可持续发展目标之一的教育领域(SDG4),以获得欧盟成员国在 2022 年的排名。使用 MIDIA 方法得出的结果与使用 TOPSIS 和 VIKOR 方法得出的结果进行了比较。研究得出结论,备选方案的排名取决于与参考点距离的重要性系数和数据设置。
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A Multi-Criteria Method Integrating Distances to Ideal and Anti-Ideal Points
Multi-criteria decision-making methods based on reference points and distances from them are essential for evaluating alternatives across multiple criteria. These methods provide structured approaches to comparing and ranking alternatives relative to specified reference points. The main objective of this paper is to present the Multi-Criteria Method Integrating Distances to Ideal and Anti-ideal Points (MIDIA), which, through a weighted system, allows for the consideration of balance and asymmetry in assessing alternatives based on their distances from the ideal and anti-ideal points. As a multi-criteria algorithm, MIDIA is user-friendly and reflects the human mind’s natural tendency to assess objects based on fundamental concepts—comparison with the ideal solution and the anti-ideal solution—that are familiar from everyday experiences and provide valuable insights from a behavioral perspective. Moreover, the proposed method can be seen as an extension of Hellwig’s approach, designed to facilitate the ranking of alternatives based on two reference points: the ideal point and the anti-ideal point, measuring the distance between the alternative and the ideal point and the distance between the ideal and anti-ideal points. The MIDIA method integrates elements from both TOPSIS and VIKOR, by incorporating the structure of TOPSIS and the compromise perspective of VIKOR, offering a balanced approach to multi-criteria decision-making by focusing on the distances from ideal and anti-ideal points. Illustrative examples are given to demonstrate the usability of the proposed tool in situations where the decision-maker has asymmetrical preferences concerning the importance of ideal and anti-ideal points in ranking alternatives. Moreover, the MIDIA method is applied to one of the Sustainable Development Goals, in the area of education (SDG4), to obtain the rankings of EU member countries in 2022. The results obtained using the MIDIA method were compared with those obtained using the TOPSIS and VIKOR approaches. The study concludes that the ranking of alternatives depends on the coefficients of the importance of the distances to reference points and the data setup.
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