Fractional Solid Transportation Problem under Fermatean Fuzziness: An SDR Decomposition and Optimization Algorithm

Author(s)	Ms. Nancy J E, Dr. Jeyakumar. S
Country	India
Abstract	This paper presents a structured optimization framework for the Fermatean Fuzzy Fractional Solid Transportation Problem (FFFSTP), a three-dimensional decision model involving sources, destinations, and routing alternatives under uncertainty. The proposed methodology initially ensures model feasibility through balance verification and necessary adjustments. All Fermatean fuzzy parameters are systematically transformed into crisp equivalents using an appropriate grade function to facilitate computational tractability. The fractional objective function is decomposed into numerator and denominator components, each optimized independently using a refined Source–Destination–Routing (SDR) tableau approach. The optimization process incorporates reduction techniques and iterative adjustment mechanisms to maintain feasibility across all constraints. The final solution is obtained by integrating the optimized components, resulting in an efficient and consistent allocation strategy. The proposed approach provides a robust framework for solving complex transportation problems in advanced fuzzy environments.
Keywords	Fermatean fuzzy sets; Fractional solid transportation problem; SDR tableaux; Decomposition algorithm; Three-dimensional transportation.
Field	Mathematics
Published In	Volume 8, Issue 2, March-April 2026
Published On	2026-03-27

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