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Optimization Framework for Intuitionistic Fuzzy Transportation Problem Solutions

DOI https://doi.org/10.55640/ijctisn-v03i10-01
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Faisal Abdullah Al-Harbi 1 ,
4 Department of Cybersecurity, Saudi Institute of Computing and Information Security, Riyadh, Saudi Arabia

Abstract

Transportation problems constitute a fundamental class of optimization models for determining cost-effective allocation of commodities from multiple sources to multiple destinations. Conventional transportation models, however, generally assume that transportation costs, supply capacities, and destination requirements are known precisely. Such assumptions are often unrealistic when decision-makers operate with incomplete, ambiguous, or hesitant information. Intuitionistic fuzzy sets provide a suitable mathematical environment for representing both membership and non-membership information and therefore offer greater flexibility than conventional fuzzy representations. This paper develops an optimization framework for determining effective solutions to intuitionistic fuzzy transportation problems. The proposed framework integrates intuitionistic fuzzy representation, normalization, ranking-based comparison, initial feasible solution construction, and iterative optimization. The methodological design is positioned within the existing literature on triangular, type-2, fully intuitionistic, multi-objective, and specialized transportation models. Particular attention is given to the computational requirements of converting intuitionistic fuzzy transportation parameters into comparable decision values while retaining uncertainty information as far as practically possible. A hypothetical transportation scenario is used to demonstrate the functional logic of the framework. The analysis indicates that an integrated optimization procedure can improve solution consistency, facilitate comparison among competing transportation plans, and provide a more systematic basis for decision-making under uncertainty. The framework also highlights important limitations associated with defuzzification, ranking sensitivity, computational complexity, and the loss of some uncertainty information during numerical transformation.

Keywords

Intuitionistic Fuzzy Sets, Transportation Problem, Optimization Framework

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