إبراهيم عبد الله تنتوش2026-08-052026-08-05https://dspace.academy.edu.ly/handle/123456789/2496This chapter is devoted to the concepts that we need in the following chapters. The materials in this chapter are taken from the following references: [2], [3], [5], [6], [7], [9], [10], [16], [17], [18], [19], [20], [22], [23], [26], [27], [28],[29], [30], [33], [34], [35], [36], [37], [38]. 1.1 Relations: Some describe or define mathematics as the study of relations. Since a relation is a set of ordered pairs, we get our first glimpse of the fundamental importance of the concept of an ordered pair. Definition 1.1.1: If A and B are any non-empty sets, then the product (or Cartesian product ) A × B is defined by: 𝐴×𝐵={(𝑎,𝑏):𝑎∈𝐴,𝑏∈𝐵}. Definition 1.1.2: A binary relation or simply a relation R from a set A into a set B is a subset of A × B, and we write that 𝑎𝑅𝑏 or (𝑎,𝑏)∈𝑅 .This study is devoted to the concept of intuitionistic fuzzy interior ideals of Г-semigroup, by using Atanssov's idea and investigate some of their important properties.We will see a characterization of a simple Г-semigroup in terms of intuitionistic fuzzy interior idealsخواص المثاليات الداخلية