Le, T.H.P.; Chu, T.-C. Novel Method for Ranking Generalized Fuzzy Numbers Based on Normalized Height Coefficient and Benefit and Cost Areas. Axioms2023, 12, 1049.
Le, T.H.P.; Chu, T.-C. Novel Method for Ranking Generalized Fuzzy Numbers Based on Normalized Height Coefficient and Benefit and Cost Areas. Axioms 2023, 12, 1049.
Le, T.H.P.; Chu, T.-C. Novel Method for Ranking Generalized Fuzzy Numbers Based on Normalized Height Coefficient and Benefit and Cost Areas. Axioms2023, 12, 1049.
Le, T.H.P.; Chu, T.-C. Novel Method for Ranking Generalized Fuzzy Numbers Based on Normalized Height Coefficient and Benefit and Cost Areas. Axioms 2023, 12, 1049.
Abstract
To avoid loss of information and incorrect ranking, this paper proposes a method for ranking generalized fuzzy numbers, which guarantees both horizontal and vertical values are important parameters affecting the final ranking score. In this method, the normalized height coefficient is introduced to evaluate the influence of the height of fuzzy numbers on the final ranking score. The higher the normalized height coefficient of a fuzzy number is, the higher its ranking. The left area and the right area are presented to calculate the impact of vertical value on the final ranking score. The left area is considered the benefit area. The right area is considered the cost area. The fuzzy number is preferred if the benefit area is larger and the cost area is smaller. The proposed method can be employed to rank both normal and non-normal fuzzy numbers without normalization or height minimization. Numerical examples and comparison with other methods highlight the feasibility and robustness of the proposed method, which can overcome the shortcomings of some existing methods and can support decision-makers to select the best alternative.
Keywords
generalized fuzzy numbers; ranking; normalized height coefficient; left area; right area
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
