A Multi-Criteria Method Integrating Distances to Ideal and Anti-Ideal Points

Abstract

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.