Modify Symmetric Fuzzy Approach to Solve the Multi-Objective Linear Fractional Programming Problem

1. Introduction

The linear fractional programming problem has been a topic of great importance in nonlinear programming, in the military. Programming games have this form when troops are in the field. The decision to be taken has something to do with how to distribute the fire among several possible types of targets. The fractional programming method is useful in solving the problems in economics whenever the different economic activities utilize the fixed resources in proportion to the level of their values. In the financial analysis of a firm, the purpose of optimization is to find the optimum of a specific index number, which is usually the most favorable ratio of revenues and allocation.

Fuzzy linear fractional programming problems (FLFPPs) has been a stimulating research area in recent years. Many authors have discussed the use of fuzzy optimization and fuzzy linear programming e.g. Li et al. (2009) study focus on fractional programming methodology for multi-attribute group decision-making using IFS. Li (2010) present a techniaue TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. Li (2011) study depend on closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information "." Yu et al. (2021) introduce an intuitionistic fuzzy multi-objective goal programming approach to portfolio selection ".". Li and Cheng (2004) present stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints.

Bellman and Zadeh (1970) introduce fuzzy gaols and fuzzy constraints can be simplified precisely as fuzzy sets in space of alternative. A “fuzzy decision”, then, might be observed as an interchange of the assumed goals and restraints. A superior decision is clear as a fact in the space of alternative at which the grade of membership of a fuzzy decision attains its supreme value. Dhiman and Kumar (2017) present a novel bio-inspired based metaheuristic technique for engineering applications. Dhiman and Kumar (2018) study a bio-inspired algorithm for engineering problems. Kaur et al.(2020) established a new approach a new bio-inspired based metaheuristic paradigm for global optimization. Dhiman and Kaur (2019) introduce a bio-inspired based optimization algorithm for industrial engineering problems. Kumar and Dhiman (2021) present a comparative study of fuzzy optimization through fuzzy number. Chatterjee (2021) review and discussions an Artificial Intelligence and Patentability. Vaishnav et al. (2021) present an analytical review analysis for screening covid-19. Gupta et al (2022) proposed a study crime tracking system and people’s safety in India using machine learning approaches.T. Sharma et al. (2022) review and discussions a breast cancer image classification using transfer learning and convolutional neural network. Shukla et al. (2022) Self-aware Execution Environment Model (SAE2) for the Performance Improvement of Multicore Systems. Dhiman et al. (2021) proposed a novel algorithm for global optimization: rat swarm optimizer. Dehghani et al. (2020) A new approach optimization technique based on darts game. Dhiman (2021) present a hybrid bio-inspired metaheuristic optimization approach for engineering problems.