Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

¹ Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, West Bengal, India
² Faculty of Engineering Management Poznan University of Technology, ul. Jacka Rychlewskiego 2, 60-965 Poznan, Poland
³ IAM (UME), Middle East Technical University, 06800 Ankara, Turkey

^* Corresponding author: sankroy2006@gmail.com

Received: 27 December 2020
Accepted: 3 May 2021

Abstract

This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.