Preliminaries

This chapter presents an exploration of foundational concepts in the domain of uncertainty modeling through different types of fuzzy sets such as type-2 fuzzy sets, triangular interval type-2 fuzzy sets, simplifiedNeutrosophic set neutrosophic setsSimplified neutrosophic set, and triangular fuzzy hesitant fuzzy setsTriangular fuzzy hesitant fuzzy set. Algebraic operations, including addition, subtraction, multiplication, and division, are defined for all the given fuzzy sets extensions. The concepts of score and deviation functions are defined also defined to facilitate comparisons and ordering among sets. The extensions of fuzzy sets introduced in this chapter provide preliminaries to the methods applied in the upcoming sections and are presented in the order they appear in the chapters for the reader's comprehension.