Hosseinzadeh Lotfi, F.Allahviranloo, T.Pedrycz, W.Shahriari, M.Sharafi, H.Razipour, GhalehJough, S.2024-05-192024-05-1920231860-949Xhttps://doi.org/10.1007/978-3-031-44742-6_2https://hdl.handle.net/20.500.12713/4478This chapter explores the fundamentals of fuzzy theory and introduces the concept of fuzzy type-2. Fuzzy sets, which allow for handling uncertainty and vagueness in data, are discussed as an extension of traditional binary set theory. Arithmetic operations on fuzzy sets, such as union, intersection, and complement, enable logical reasoning and informed decision-making based on fuzzy information. The chapter also covers triangular and trapezoidal fuzzy numbers, which provide a means to represent imprecise and uncertain quantities. These fuzzy numbers are essential for quantifying and reasoning with fuzzy data, with applications in various domains for modeling real-world phenomena. Furthermore, the chapter focuses on the ranking of fuzzy numbers using different functions. Techniques and tools for ranking fuzzy numbers are examined, offering insights into comparing and ordering fuzzy data based on their degrees of membership and uncertainty. This information is valuable for decision-making processes when dealing with fuzzy information. Overall, the chapter provides a comprehensive introduction to fuzzy theory and its practical applications, particularly in fuzzy type-2. By understanding fuzzy sets, arithmetic operations, triangular and trapezoidal fuzzy numbers, and the ranking of fuzzy numbers, readers gain a solid foundation in utilizing fuzzy logic and reasoning. This knowledge empowers them to make more informed decisions in domains where imprecise and uncertain data are prevalent. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.eninfo:eu-repo/semantics/closedAccessBook Chapter112157822-s2.0-8518467772910.1007/978-3-031-44742-6_2N/A