A new Fermatean fuzzy multi-objective indefinite quadratic transportation problem with an application to sustainable transportation

Abstract

In this work, a Fermatean fuzzy (FF) multi-objective indefinite quadratic transportation problem (TP) is introduced. Due to some unavoidable reasons, real-life transportation parameters such as supply, demand and costs are indeterminate in nature and cannot be expressed in crisp terms. We represent these parameters using FF numbers, an extension of fuzzy numbers, which are capable of representing indeterminacy efficiently. A multi-objective indefinite quadratic TP where each objective is a product of two linear factors (cost functions) is considered. Defuzzification of FF numbers is accomplished by the introduction of (Formula presented.) -cut for the first time. The obtained crisp TP is solved using the intuitionistic fuzzy programming approach and FF programming approach to arrive at a compromise solution. To substantiate the work, solution methodology based on defuzzification using the ranking function is also deliberated. The applicability of the model is demonstrated through a sustainable TP, which simultaneously minimizes transportation cost with depreciation cost and packaging cost with wastage cost. The resulting value of the objective functions and the aspiration levels are compared to depict the efficacy of the proposed method over the ranking function method. The concluding section summarizes the work, and future avenues along with some limitations of the work are also specified.