Optimization of fuzzy bottleneck cost transportation models in the decision framework of congruence modulo technique

Abstract

This article investigates the Congruence Modulo algorithm and time freezing method as innovative solutions for addressing fuzzy bottleneck cost transportation problems. Starting from the crisp bottleneck cost transportation problem, we extend this framework into a fuzzy domain, applying the proposed methodology to both cost and time parameters represented through triangular fuzzy numbers in symmetric and non-symmetric forms. The complex fuzzy expressions are systematically transformed into crisp pointwise problems, which are then solved using the integrated approach of the congruence modulo and time freezing methods. The results validate the approach’s effectiveness by achieving objective values that align with or improve upon established methods. The findings underscore this method's practical and robust capability to optimize complex transportation problems under conditions of fuzziness and uncertainty.