الفهرس 
ContentsOnly 14 pages are availabe for public view
 |  | from | 279 |  |  |
| | | from | 279 | | |
Abstract
In this thesis, we make some contributions to the soft set theory and soft topology. First, we initiate and investigate two new types of relations between ordinary points and soft sets, namely partial belong and total non-belong relations. They somewhat express the degree of membership and non-membership of an element. Second, we apply those relations to give a real-life application on the area of optimal choices and to define new types of soft separation axioms, namely $tt$-soft $T_i$-spaces, $pt$-soft $T_i$-spaces and $pp$-soft $T_i$-spaces $(i=0, 1, 2, 3, 4)$. The desire of generalizing some set-theoretic properties to the soft set theory motivated us to define and discuss the concepts of $T$-soft subset and $T$-soft equality relations. In addition, we study the soft version of increasing, decreasing and monotonic sets which represent the cornerstone of soft topology in the ordered setting. Third, we prove the equivalence between the concepts of enriched and extended soft topologies and derive they are a sufficient condition to satisfy the interchangeable property of interior and closure operators between soft topology and its parametric topologies. This interesting result helps us to study the relationships between the topological concepts on crisp and soft settings. Fourth, we exploit increasing and decreasing soft sets to formulate the concepts of soft topological ordered spaces and explore some soft ordered separation axioms, namely $ttn$-soft $T_i$-ordered, $tpn$-soft $T_i$-ordered and $tpo$-soft $T_i$-ordered spaces $(i=0, 1, 2, 3, 4)$. In general, we study the rudiments of these soft ordered spaces and show the relationships among them with the help of illustrative examples. Fifth, we introduce the concepts of soft continuous, open, closed and homeomorphism mappings on soft ordered setting and reveal their main properties. Then, we generalize those soft mappings using celebrated generalized soft open sets. Sixth, we apply monotonically soft sets to explore new types of soft compactness on the finite spaces called monotonically soft compact and ordered soft compact spaces. In addition, we provide an application on how to expect the missing values of objects on the information system depending on ordered soft compact spaces. Finally, we relax the conditions of soft topological ordered spaces to define the concept of supra soft topological ordered spaces. We establish its fundamental notions and define the concepts of supra $ttn$-soft $T_i$-ordered spaces.