Elham Zahiri; Aghile Heidari; Ham,id Reza Yoosefzade
Abstract
The Pareto set of optimal solutions resulting from solving multi-objective optimization problems, although on the one hand increases the flexibility in choosing an optimal solution according to the conditions of a system, but on the other hand, due to different tastes and perspectives in a The system, ...
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The Pareto set of optimal solutions resulting from solving multi-objective optimization problems, although on the one hand increases the flexibility in choosing an optimal solution according to the conditions of a system, but on the other hand, due to different tastes and perspectives in a The system, choosing the most desirable Pareto front answer, can be a serious challenge. In this regard, in this article, in the first step, by defining the concept of Gaussian degree of proximity and presenting a decomposition approach based on it, we produce the Pareto front, which numerical results show that this front in comparison with fronts obtained from other quality decomposition approaches. Has a higher. In the second step, due to the lack of an evaluation criterion that examines the quality of a front from different angles, we present a new evaluation criterion for comparing different fronts, which by considering both factors of mastery and proximity to the optimal answer. Examines the quality of the answers on a Pareto front. The results obtained from the simulation of the proposed steps on the existing standard test functions confirm the efficiency and effectiveness of each of the steps of the proposed problem.
Data Envelopment Analyses
Ham,id Reza Yoosefzade; Azam Teimuri; Aghile Heidari
Abstract
The models of Data Envelopment Analysis (DEA) based on Goal Programming (GDEA) seeks to address some drawbacks of classical DEA by increasing the degree of resolution and providing real weights to Decision-Making Units (DMUs). Experimental results indicate that the GDEA models do not completely cope ...
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The models of Data Envelopment Analysis (DEA) based on Goal Programming (GDEA) seeks to address some drawbacks of classical DEA by increasing the degree of resolution and providing real weights to Decision-Making Units (DMUs). Experimental results indicate that the GDEA models do not completely cope with these in some cases which are tested. Also, in calculating the optimal solution with different methods of evaluating the efficiency of units, we are faced with a group of Pareto optimal solutions that make a decision maker facing a serious challenge in choosing the most appropriate solution. To solve this, in the first step, this paper uses the concepts of fuzzy logic and then proposes the F-GDEA approach based on fuzzy logic in solving the GDEA models, which increases the resolution of the methods to rank the units. In the second step, by using the F-GDEA approach, we propose a new hybridized fuzzy approach called HF-GDEA for short, taking into account the various ranking results from the different programming models. With this new proposed approach, we combine the rankings obtained from different methods and present a new ranking for the DMUs. In other words, the HF-GDEA approach makes it possible to compare and thus select an optimal solution from Pareto's optimal solutions set. Finally, the proposed approach is applied to two practical examples and their numerical results are presented.