Interval-Valued Complex Neutrosophic Sets and Complex Neutrosophic Soft Topological Spaces

Network performance is the evaluation and assessment of collective network statistics, to define the quality of services offered by the computer network. It is a qualitative and quantitative technique that measures and defines the performance level for a network. Networking provides a link between different factors (bandwidth, number of devices, network traffic and latency) for performing multiple tasks. These factors affect the network speed and quality. Some errors occur due to network traffic and latency can produce uncertain results. These results provide low quality and speed in the network that caused time wasting with no required results. In this regard, the notion of interval valued complex neutrosophic relation (IVCNR) is developed to handle this situation. Modeling problems by using the idea of interval valued complex neutrosophic sets (IVCNSs) and interval valued complex neutrosophic relations (IVCNRs) will not only formulate the effects of one factor to other but also defines the grades of membership, abstains and non-membership. The cartesian product among two IVCNSs and the types of IVCNRs is discussed. By applying the methods of IVCNRs on the factors of network performance that can produce better network speed and improved quality in the network. In continuation this study introduced and investigates the structure of complex neutrosophic soft topological spaces. The foundational definitions of complex neutrosophic soft topology, open and closed sets, interior, closure, and boundary are formally established. The study also explores the concept of complex neutrosophic soft bases and subspace topologies, along with criteria for basis generation and topological refinement. Several theorems elucidate the relationships among topological constructs and operations such as union, intersection, and complementation under complex neutrosophic soft conditions. We apply pervious methods on these problems and collect some results. But through this method, the required results achieved more reliable than the previous methods. So, the proposed method is the best method for modeling uncertain complexities in the required results. Some applications are also given that can be applied in our day to day life.