Ph.D Theses

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Browsing Ph.D Theses by Subject "Mathematics"

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    Operation Approach on 𝜶𝒈-Open Sets and Neutrosophic Soft Open Sets
    (Avinashilingam, 2024-03) Mershia Rabuni J J; Dr. N. Balamani
    The concept of operation on topology was initially introduced by Kasahara in the year 1979. In 1991, Ogata utilized the idea of operation approach and defined a new form of sets stronger than open sets called γ-open sets in topological spaces. Following his work, many researchers has contributed to the theory of operation approach by studying the properties of operation on various collection of open sets in topological spaces. Few researchers has introduced the concept of operation approach in different topological spaces also. The class of α-generalised closed sets lies between the class of generalized α-closed sets and the class of generalised semi-closed sets. The study on op- eration approach on α-generalised open sets broadens the area of research on operation approach by analysing the topological behaviours in a detailed manner. The study mainly focuses on the change in the topological properties that occurs when the operation is defined on a non topological collection. By using the oper- ation on α-generalised open sets, αgγ -open sets are introduced. The dependency and independency relation between various existing different types of open sets via γ-operation are determined. The topological properties of the operators such as interior, closure, kernel using operation on αg-open sets are examined. New forms of separations axioms are constructed using operation on αg-open sets and some characterization theorems for the separation axioms are derived. Analy- sis of continuous maps using γ-operation on αg-open sets and αgγ -open sets are carried out. The concept of operation is extended to neutrosophic soft topologi- cal space and the properties of the operation on neutrosophic soft open sets are analysed in neutrosophic soft environment. A decision making problem is chosen and priority attribute based decision making algorithm is proposed for solving the chosen problem using γ-operation on neutrosophic soft open sets. Moreover, to reduce the computation for determining union, intersection, closure and interior in neutrosophic soft environment, programs are developed using python. Finally, a python program for the proposed decision making algorithm is also constructed in neutrosophic soft environment.