Solving multi-level multiobjective fractional programming problem with rough interval parameter in neutrosophic environment

¹ Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India
² Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore 560059, India
³ Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
⁴ School of Science, College of Sciences, Technology, Engineering, Mathematics, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia .

^* Corresponding author: ashafiq@ksu.edu.sa

Received: 21 June 2020
Accepted: 21 July 2021

Abstract

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.