A Direct Method for Solving Intuitionistic Linear Programming problems

The omnipresent uncertainty inherent in real-world problem-solving endeavors often renders the attainment of optimal solutions a prolonged and occasionally insurmountable task. To address this challenge, we advocate for applying Intuitionistic Sets Theory, an extension of Fuzzy Sets Theory tailored for scenarios with incomplete information. This paper introduces an Intuitionistic Linear Programming (ILP) model, utilizing triangular Intuitionistic numbers to represent parameters and acknowledging the complexities of incomplete information. The proposed ILP problems, employing a ranking function, can be systematically transformed into crisp models, facilitating resolution through standard optimization methods. This study represents a significant advancement in decision science by providing a nuanced framework combining Intuitionistic Sets Theory and Linear Programming to address uncertainty, offering theoretical enrichment and practical applicability to complex real-world challenges.