Covering based rough set theory

The beginning of the rough set theory is known as information systems that relate objects and their properties. Objects that have the same properties are indiscernible from each other. The indiscernible object pairs define an equivalence relation on the set of objects. The set of equivalence classes depending on the properties of each object creates a partition of the set of objects. The partition obtained is a special cover of the universal set and this situation may be restrictive in scientific research. The concept of covering, which is a generalization of partition, is given in order to spread scientific studies to a wider area. Thus, the foundations of the covering based rough set theory are laid. Covering based rough set theory; transcends the limits of the conventional classical set theory. The purpose of this thesis is; to examine the element based, particle based and subsystem based definitions and properties of the approach operators with the concept of covering and to reveal the relationships between them.