Title: On duality of fuzzy multiobjective optimisation problems: application to a multiplicative search technique

Authors: Mohamed Abd El-Hady Kassem; Mohamed Abd Allah El-Hadidy

Addresses: Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt ' Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: In this paper, we present a new study to minimise the expected value of the first meeting time between one of the searchers and the randomly moving target in the space (case of the multiplicative search technique) from a viewpoint of computational optimisation. We introduce the dual problem for the fuzzy multiobjective nonlinear programming problem (FMONLP) with inequality constraints which is obtained in El-Hadidy [International Journal of Computational Methods, Vol. 13, No. 6 (2016) 1650038 (38 pages)]. For this problem, we generalise the following classes of the vector-valued functions for fuzzy sets: weak strictly pseudo-quasi type I, strong pseudo-quasi type I, weak quasi strictly type I and weak strictly pseudo type I. We provide the fuzzy forms of Mond-Weir and general Mond-Weir duals for the involved problem and consequently various duality results are derived.

Keywords: multiplicative search technique; convex fuzzy mappings; invex fuzzy mappings; multiobjective nonlinear programming; weak strictly pseudo type I.

DOI: 10.1504/IJMOR.2018.090803

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.3, pp.364 - 377

Received: 03 Nov 2015
Accepted: 13 Oct 2016

Published online: 28 Mar 2018 *

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