On SR-fuzzy Transportation Problem Models and their Solution Algorithm

Businesses have been focusing on the need to increase profit by reducing operational costs. In operations research, the transportation problem is essentially a logistics puzzle focused on moving goods from various suppliers to their final destinations as efficiently as possible. By balancing availability constraints with customer requirement, this model identifies the specific shipping routes that will either drive down total costs or boost the bottom line. In this paper, we explore a transportation model where availability, requirement, and shipping costs are all treated as square root (SR)-fuzzy numbers. The majority of existing studies regarding fuzzy transportation issues revolve around intuitionistic, Pythagorean, and Fermatean fuzzy numbers, leaving other fuzzy frameworks less explored. However, the current study is the first to consider the fuzzy parameter as square root fuzzy numbers. A transportation problem is formulated along with the corresponding algorithms that are applicable to SR-fuzzy data. A key contribution of this work is the formulation of a unique score function designed to the specific characteristics of SR-fuzzy sets. Unlike the conventional score function, the proposed score function takes non-negative values. We integrate this score function with standard SR-fuzzy arithmetic to build a method for solving transportation problems in SR-fuzzy environment.