Open AccessOn Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands
Author(s) -
Namrata Rani,
Vandana Goyal,
Deepak Gupta
Publication year - 2021
Publication title -
international journal of mathematical, engineering and management sciences
Language(s) - English
Resource type - Journals
ISSN - 2455-7749
DOI - 10.33889/ijmems.2021.6.6.096
Subject(s) - mathematical optimization , quadratic programming , mathematics , fractional programming , quadratic equation , sequential quadratic programming , fuzzy logic , hierarchy , set (abstract data type) , quadratic model , flowchart , active set method , computer science , nonlinear programming , artificial intelligence , nonlinear system , statistics , physics , geometry , response surface methodology , quantum mechanics , economics , programming language , market economy
This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.