A Study on Trapezoidal Neutrosophic Fuzzy Optimization Problems Using Interval Based Approaches

Abstract

Decision-making is a fundamental process for organizations and individuals for their newlinesurvival in a highly competitive environment. Mathematical optimization is an newlineapproach that significantly enhances decision-making in various domains. In real-world newlinescenarios, the choice of parameters are not definitive due to several factors such as newlinedata inaccuracy, inadequate information, imprecision of physical models, parameter newlinefluctuations and calculation errors. Consequently, the incorporation of uncertainty and newlineimprecision is essential for modeling real-world problems. In such situations, fuzzy newlineset theory can be utilized to consider uncertainties and it highly influenced decisionmaking. newlineFurther, neutrosophic fuzzy sets, provide an improved structure to represent newlineuncertainty, indeterminacy, and imprecision in practical optimization challenges. The newlinethree components (truth, indeterminacy, and falsity) provide a flexible representation of newlineuncertainty compared to fuzzy sets in practical situations. newlineThis thesis introduces an interval-based de-neutrosophication technique that newlineeffectively converts neutrosophic fuzzy numbers into intervals to improve the applicability newlineof optimization techniques. Further, Sengupta and Pal s ranking methodology for interval newlinenumbers are used to rank neutrosophic fuzzy numbers. The research addresses trapezoidal newlineneutrosophic fuzzy optimization problems with interval optimization techniques. The newlineresearch covers Linear Programming Problems, Transportation Problems, Multi-objective newlineTransportation Problems, and Assignment Problems. Also, the research provides Multi- newlineCriteria Decision-Making methodologies to assess the quality of groundwater in practical newlinedomain. The use of interval numbers into these approaches enhances the problem handling newlineand it results a suitable and realistic solutions in uncertain environment. This thesis seeks newlineto enhance the practical applications by providing novel perspectives on neutrosophic newlinefuzzy numbers to tackle complex real-world decision-making and optimization problems