A Fuzzy Optimization Technique for Multi-Objective Aspirational Level Fractional Transportation Problem

Abstract

In this research work, a soft computing optimization operating approach is developed for a multi-objective aspirational level fractional transportation problem. In the proposed technique, a mathematical model is formulated for the multi-objective aspirational level fractional transportation problem (MOFTP) based on the highest value of one and all objectives of the model. We also used the symmetry concept over our model to identify the best optimum solution based on symmetrical data. We constructed the membership grades for the set of fetched parameters having symmetry. In this work, we also used the concept of ranking function in our mathematical model to obtain the optimum solution of the fuzzy multi-objective fractional transportation. In this proposed algorithm, the aspiration levels are also associated with the objective function of MOFTP. We are also proposing a new approach for the optimization of fractional problems in which the objectives are being optimized by using the numerator function and denominator function simultaneously. Further, a methodology is also developed to find the average cost for each fractional objective of the model. After that, we will find the ranking function for each parameter by using the defuzzification method. By this methodology, we will be able to convert the MOFTP into a bi-objective transportation problem. The provided technique is elaborated with the help of numerical computations to prove the beauty and power of the proposed technique.

Solving Fuzzy Nonlinear Programming Problems With Exterior Penalty Fuzzy Valued Functions

“…After this transformation, they apply standard search techniques like the exterior penalty function method and the interior penalty method to find solutions. Sharma et al (2021Sharma et al ( , 2022 have introduced a new approach for addressing multi-objective aspirational level fractional transportation problems involving fuzzy parameters. They also proposed a Fermatean fuzzy ranking function in optimization of intuitionistic fuzzy transportation problems.…”

Decision-making support for optimizing pollutant degradation processes in domestic wastewater treatment plants involving uncertain parameters via fuzzy programming approaches

“…This approach represents uncertain parameters as fuzzy variables with membership functions defined by managers. Fuzzy programming models have been reported as a powerful tool in decision-making problems in various fields, such as photovoltaic panel designs [20], energy or power management [21][22][23][24], supply chain management [25][26][27][28], advanced manufacturing processes [29], and many more.…”

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

“…Further, Das and Mandal [11] as well as Das et al [12] converted FLFPPs into crisp multiobjective LFPPs, which were then solved to obtain a solution. In one of their studies, Sharma et al [13] considered multiobjective fractional programming problems for fixed aspiration levels using symmetric fuzzy parameters. Dutta et al [14,15] worked on the sensitivity of FLFPPs and also investigated the impact of tolerance on both LFPPs and FLFPPs.…”