A novel indeterminacy-based score function for fermatean fuzzy sets with application to multi-objective solid transportation optimization

Abstract

Transportation planning in real life is never perfect-costs fluctuate, supply levels shift, and demand is rarely predictable. Motivated by this practical reality, we propose a Fermatean Fuzzy Programming (FFP) approach to solve the Multi-Objective Solid Transportation Problem (MOSTP) under uncertainty. Unlike standard transportation models that consider only supply and demand, the Solid Transportation Problem also accounts for conveyance capacity, bringing it closer to how logistics actually works. We adopt the Fermatean Fuzzy Sets framework because its cubic constraint on membership and non-membership degrees covers a wider uncertainty space than both Intuitionistic and Pythagorean Fuzzy Sets. One key contribution of this work is a new score function that directly incorporates the indeterminacy degree and is proved to always stay within $[0, 1],$ giving more reliable rankings than existing functions. Using this score function, all uncertain parameters are converted to crisp values and the problem is solved through the FFP model to reach a meaningful compromise solution. Comparisons with Type(i) and Type(ii) score functions from the literature clearly confirm that our approach performs better across all tested criteria.