Interactive TOPSIS algorithms for solving multi-level non-linear multi-objective decision-making problems

Document Type : Original Article

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Department of Basic Sciences, Faculty of Engineering, Benha University, EL-Qalyoubia - Egypt.

Abstract

Abstract
This paper extended the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology for solving multi-level non-linear multi-objective decision-making (MLN-MODM) problems. Also, two new interactive algorithms are presented for the proposed TOPSIS approach for solving these types of mathematical programming problems. The first proposed interactive TOPSIS algorithm includes the membership functions of the decision variables for each level except the lower level of the multi-level problem. These satisfactory decisions are evaluated separately by solving the corresponding single-level MODM problems. The second proposed interactive TOPSIS algorithm lexicographically solves the MODM problems of the MLN-MOLP problem by taking into consideration the decisions of the MODM problems for the upper levels. Illustrative example is presented in order to show the efficiency and superiority of the proposed approach and the two interactive TOPSIS algorithms.

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