Unified Optimization Approach for Intuitionistic Fuzzy Transportation Problems: Integrating FFGF and CATS-M

Naveen Kumar S1, Dr K Karuppayi2, Dr K Thanalakshmi3

1Research Scholar Department of Mathematics, Providence College for Women Coonoor,The Nilgiris.

2Assistant Professor, Department of Mathematics, Providence College for Women Coonoor,The Nilgiris.

3Associate Professor, Department of Mathematics, Kamaraj College of Engineering and Technology,

SPGC Nagar K Vellakulam ,Virudhunagar.

Abstract

            Establishing a novel approach to solve the transportation problems in a Fermatean fuzzy environment is the goal of this work. This research addresses the Transportation Problem (TP) under imprecise parameter conditions using Fermatean fuzzy sets (FFS), extending from Pythagorean fuzzy sets (PFS). In this work, Fermatean Fuzzy Grade Function (FFGF) is proposed for optimizing TP with Fermatean fuzzy parameters, targeting three types of Fermatean fuzzy transportation problems (TYPE-1 FFTP, TYPE-2 FFTP, TYPE-3 FFTP). Furthermore, the research introduces a cost-averaged transportation solution model (CATS-M) to finding basic, feasible solutions for TP, emphasizing balanced and unbalanced components. This approach utilizes the average unit cost value of columns and rows to create a maximum cost-averaged value (MCAV) table, facilitating problem-solving by balancing demand and supply. The proposed methodology is straightforward, easily comprehensible, and user-friendly. It offers a less complex alternative to well-known meta-heuristic algorithms in the literature. The study includes numerical examples to illustrate the method's efficacy, comparing results with existing approaches.

Keywords: Fermatean fuzzy transportation problem, average unit cost, grade function, balance, and unbalanced components.