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TOPSIS for bi-level MODM problems
Authors:Ibrahim A Baky  Mahmoud A Abo-Sinna
Institution:1. Department of Basic Sciences, Faculty of Engineering, Benha University, EL-Qalyoubia, Egypt;2. Department of Statistics, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia
Abstract:TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper.
Keywords:Multi-objective decision-making  Bi-level programming problems  Fuzzy programming  TOPSIS
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