An Efficient Modified Fermatean Fuzzy Data Envelopment Analysis Approach Based Fractional Transportation Problem Under Interval-Valued Fermatean Fuzzy Sets

Uncertainty is excessively a common, inevitable, and conspicuous aspect of any decision-making process, including transportation problems.Since its inception, a plethora of uncertainty representation methods has been put forward to deal with uncertainty by various researchers.Among those, fuzzy set and Intuitionistic fuzzy set is remarkably effective representation methods of uncertainty modeling.The purpose of this paper is to define a triangular interval-valued Fermatean fuzzy number (TIVFFN) and its arithmetic operations.Fractional transportation problems (FTPs) have important implications for cost reduction and service improvement in logistics and supply management.However, in practical problems, the parameters in the model are not precise due to some unpredictable factors, including diesel prices, road conditions, weather conditions and traffic conditions.To address these challenges, we consider an FTP with TIVFFN as its parameter and call it an interval-valued Fermatean fuzzy fractional transportation problem (IVFFFTP).Here the proposed Modified Fermatean fuzzy Data envelopment analysis (MFFDEA) method for solving this IVFFFTP is proposed without re-transforming the original problem into an equivalent crisp problem.The objective of this work is to investigate the TP with interval-valued Fermatean fuzzy costs in the presence of numerous conflicting objectives.A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques.Moreover, the advantages of the proposed method are also discussed.