Soft intersection (almost) bi-interior ideals and weak-interior ideals, soft intersection almost subsemigroups and ideals, bi-quasi ideals and tri-bi-ideals of semigroups

Soft set theory, introduced by Molodtsov in 1999 to model uncertainty and has shown progress with wide-ranging studies in a lot fields. One of these studies is proposing the concepts of different types of soft intersection ideals of semigroups using soft sets in semigroup theory and examination of their basic properties. In this thesis, various soft intersection ideals and soft intersection almost ideals of semigroups are presented to contribute to soft set theory. In the first section of this thesis, which consists of eleven sections, the existing studies in the literature related to semigroups and their (almost) ideals, soft sets, semigroups, and various soft intersection (almost) ideals of semigroups are mentioned. In the second section, fundamental definitions and theorems that are used in this thesis are given; the concept of soft simple* semigroup is introduced and exemplified. In the third section soft intersection weak-interior ideals of semigroups, in the fourth section soft intersection bi-interior ideals of semigroups, in the fifth section soft intersection almost subsemigroups of semigroups, in the sixth section soft intersection almost ideals of semigroups, in the seventh section soft intersection almost weak-interior ideals of semigroups, the eighth section soft intersection almost bi-interior ideals of semigroups, the ninth section soft intersection almost bi-quasi ideals of semigroups, and in the tenth section soft intersection almost tri-bi-ideals of semigroups are introduced, their properties are examined, and their examples are given. Their relationships between certain soft intersection (almost) ideals are examined in detail; and important connections between classical semigroup theory and soft set theory are presented through some key theorems and examples. Additionally, the results regarding soft set operations on these structures, as well as some conceptual characterizations of these structures such as soft image and soft inverse image, have been discussed and exemplified. Significant relationships regarding minimality, primeness, semiprimeness, and strongly primeness have been obtained between various almost ideals and soft intersection almost ideals. In the final section, the results obtained from this study are given and the importance of the results is discussed.