Diverse Fuzzy Numerical Systems and Their Utilization in the Context of Rankings

This research article explores the diverse realm of fuzzy numbers, with a specific focus on defuzzification using the bounded area method and its general applications. Fuzzy numbers, introduced by Lotfi A. Zadeh, have proven to be a powerful tool for handling uncertainty in mathematical modelling. The study begins by providing an overview of the foundational concepts of fuzzy numbers, including their types such as Triangular, Trapezoidal, Pentagonal, Hexagonal, and Heptagonal fuzzy numbers. The core of the research delves into the defuzzification process, with a particular emphasis on the bounded area method. This method, introduced for defuzzifying fuzzy numbers, offers a systematic approach to convert fuzzy sets into crisp values by considering the area under the membership function within a defined range. The article explores the mathematical underpinnings of the bounded area method and elucidates its application to various types of fuzzy numbers. Furthermore, the research investigates the general applications of defuzzification by the bounded area method across different domains. From its utilization in control theory to signal processing and decision-making systems, the study highlights the versatility and efficacy of this defuzzification approach. Real-world examples and case studies are presented to underscore the practical significance of employing the bounded area method in diverse applications