On solving multi-objective fully quadratic fractional optimisation model with interactive FGP approach

Abstract

Purpose

The main motive behind framing this paper is to provide a compromised solution for trapezoidal fuzzy number–multi-objective fully quadratic fractional optimisation model (TrFN-MOFQFOM) by avoiding ambiguities and confusion of decision-makers (DMs). Many researchers have used Taylor's series and parametric approach to transform fractional objective function into non-fractional ones, but Taylor's series expansion is valid only up to a neighbourhood. To avoid these extra efforts, this article suggests a methodology in which numerator of objective function is optimised under the condition of optimising denominator.

Design/methodology/approach

This paper suggests an efficient procedure to search for compromised solution of MOFQFOM with fuzzy coefficients using α-level set and FGP approach. Incomplete data in model is dealt with α-level set. Then after defuzzification, non-fractional models are built from fractional model to get optimal solution of every objective. Finally, the linear weighted sum of negative deviational variables is minimised to satisfy all objective functions up to maximum possible extent.

Findings

On applying suggested approach to the example given in end, the authors arrived at compromised solution having μO1(O1(x))=1 and μO2(O2(x))=0.71. The applied procedure requires less computational efforts and provides the preferred compromised solution.

Originality/value

This work has not been done previously by anyone. The idea being developed here of constructing non-fractional model by dealing numerators and denominators separately is completely new. 10; In the end, an algorithm, flowchart and numerical are also given to clarify the applicability of the suggested approach.

Citation

Rani, N., Goyal, V. and Gupta, D. (2022), "On solving multi-objective fully quadratic fractional optimisation model with interactive FGP approach", International Journal of Quality & Reliability Management, Vol. 39 No. 10, pp. 2286-2301. https://doi.org/10.1108/IJQRM-01-2021-0015