Title: On optimisation over the integer efficient set in fuzzy linear multicriteria programming

Authors: Ouiza Zerdani; Farida Achemine

Addresses: Faculty of Sciences, Laboratory LAROMAD, University Mouloud Mammeri of Tizi-Ouzou, Tizi-Ouzou, Algeria ' Department of Mathematics, Faculty of Sciences, University Mouloud Mammeri of Tizi-Ouzou, Tizi-Ouzou, Algeria

Abstract: The problem of optimising a linear function over the efficient set of a multiobjective linear programming problem is an important field of research and has some applications in multiple objective decision making. The main difficulty of this problem is that its feasible domain is non-convex and not described explicitly. The main purpose of this paper is to describe an efficient and finite new algorithm which provides a global R-optimal solution of the problem of optimising a fuzzy linear function over the efficient set of a fuzzy multiobjective integer linear programming (FMOILP) problem without having to search all integer R-efficient solutions. All the parameters of the considered problem are characterised by trapezoidal fuzzy numbers. The proposed approach is based first on the concept of comparison of fuzzy numbers by using ranking function and on an extension of Jorge's algorithm onto fuzzy numbers. Finally a numerical illustration is included for illustration.

Keywords: integer programming; global optimisation; optimisation over the efficient set; ranking function; trapezoidal fuzzy numbers.

DOI: 10.1504/IJMOR.2018.094847

International Journal of Mathematics in Operational Research, 2018 Vol.13 No.3, pp.281 - 302

Received: 26 May 2016
Accepted: 27 Dec 2016
Published online: 25 Sep 2018 *

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