A New Method for Solving Fully Generalized Quadratic Fuzzy Transportation Problem under Fuzzy Environment

Abstract

This paper presents a solution approach for the transportation problem (TP) in an uncertain environment using trapezoidal intuitionistic fuzzy numbers (TrIFNs). We introduces a new approach to solving Transportation Problems (TP) in uncertain environments, focusing on the Trapezoidal Fermatean Fuzzy Number (TrFFN). The Fermatean Fuzzy TP (FFTP) treats transportation cost, supply, and demand as TrFFN, offering superior performance and feasibility compared to existing methods. It also highlights its advantages in uncertain environments. Using standard LP algorithms, the IFTP is converted into a deterministic linear programming (LP) problem. The quadratic fuzzy transportation problem is a significant problem in operations research and optimization, involving finding the best feasible solution for a transportation problem with quadratic function cost coefficients. The paper presents a new method for solving the fully generalized quadratic fuzzy transportation problem under an ambiguous environment, considering uncertainties and fuzziness inherent in real-world transportation scenarios. The paper also addresses the minimum spanning tree (MST) problem, which involves a graph with either trapezoidal or triangular fuzzy numbers assigned to each arc length. The graded mean integration representation of fuzzy numbers is used to solve these problems. The paper proposes an alternative undefined outranking method by extending the Elimination Et Choix Traduisant La Realite (ELECTRE 1) Method method to consider uncertain, imprecise, and linguistic assessments a group of decision-makers provides. The report addresses the gap in the Electre 1 literature for problems involving conflicting systems of criteria, uncertainty, and imprecise information.

GANITJ. Bangladesh Math. Soc. 44.1 (2024) 99–106