A Study on Optimization Problems Under Various Interval Valued Intuitionistic Fuzzy Environments

Abstract

This study emphasizes the development of advanced techniques for addressing newlineoptimization problems in uncertain environments. The topics that are addressed newlineinclude Linear Programming Problems, Transportation Problems, Multi-Objective newlineTransportation Problems, Assignment Problems, and Shortest Path Problems, in terms newlineof Trapezoidal Intuitionistic Fuzzy Numbers and Interval-Valued Intuitionistic Fuzzy newlineNumbers. A novel methodology is presented that utilizes interval arithmetic operations newlinedirectly on Interval-Valued Intuitionistic Fuzzy Numbers, eliminating the need for newlineconversion to crisp values, thereby maintaining the inherent uncertainty and yielding more newlineprecise outcomes. The study also applies Multi-Criteria Decision-Making approaches to newlinereal-world scenarios, including water quality evaluation. These techniques employ the newlinecombination of fuzzy theory and optimization to assess delicate situations for decisionmaking newlinewithin interval-valued intuitionistic fuzzy domains. The results demonstrate the newlineefficacy of the presented methods in handling imprecise data and enhancing the accuracy of newlinethe solutions. The results substantially enhance the domain of optimization and decisionmaking newlineby introducing persistent and effective frameworks that address uncertainty, newlineproviding practical applications for diverse scientific and technical fields newline