Extensions of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure |
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Authors: | Mahmoud A Abo-Sinna Azza H Amer Ashraf S Ibrahim |
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Institution: | 1. Department of Basic Engineering Sciences, Faculty of Engineering, El-Menoufiya University, Shebin El-Kom, Egypt;2. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt |
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Abstract: | This paper focuses on multi-objective large-scale non-linear programming (MOLSNLP) problems with block angular structure. We extend the technique for order preference by similarity ideal solution (TOPSIS) to solve them. Compromise (TOPSIS) control minimizes the measure of distance, provided that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of “closeness” LP-metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure. The concept of a membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Moreover, we derive a single objective large-scale non-linear programming (LSNLP) problem using the max–min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in this paper. |
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Keywords: | Large scale systems Multi-objective decision making Fuzzy set theory Compromise (satisfactory solution) Positive ideal solution Negative ideal solution |
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