Fuzzy rough bi-level multi-objective nonlinear programming problems

Fuzzy rough bi-level multi-objective nonlinear programming problem (FRBMNPP) moved toward becoming rise normally in various real applications. In this article we develop bi-level multi-objective nonlinear programming problem (BMNPP), in which the objective functions have fuzzy nature and the constra...

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Bibliographic Details
Published in:Alexandria engineering journal Vol. 58; no. 4; pp. 1471 - 1482
Main Authors: Elsisy, M.A., El Sayed, M.A.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2019
Elsevier
Subjects:
Bi-level optimization
Fuzzy sets
Karush-Kuhn-Tucker (KKT) method
Multi-objective programming
Rough set
TOPSIS
Karush-Kuhn-Tucker (KKT) method
Fuzzy sets
Multi-objective programming
Bi-level optimization
TOPSIS
Rough set
ISSN:1110-0168
Online Access:Get full text
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Summary:Fuzzy rough bi-level multi-objective nonlinear programming problem (FRBMNPP) moved toward becoming rise normally in various real applications. In this article we develop bi-level multi-objective nonlinear programming problem (BMNPP), in which the objective functions have fuzzy nature and the constraints represented as a rough set. The fuzzy objective functions converted into deterministic ones by utilizing the α-cut methodology. Thus the FRBMNPP become a rough BMNPP which is transformed into two problems corresponding to the upper and lower approximation models. The Karush-Kuhn-Tucker (KKT) method and two models of technique of order preferences by similarity to ideal solution (TOPSIS) approach are developed to solve such problem. At last, applicability and efficiency of the two TOPSIS models and KKT method, suggested in this study, are presented through an algorithm and a numerical illustration.
ISSN:1110-0168
DOI:10.1016/j.aej.2019.12.002