Mathematical Investigation of Communication and Network Securities Under Interval-Valued Complex Spherical Fuzzy Information

The goal of this study is to provide a framework for a novel concept, which is highly effective at expressing ambiguous information in two dimensions. As a result, of the absence of a neutral degree in interval-valued complex Pythagorean fuzzy sets, we developed the theory of interval-valued complex spherical fuzzy sets. Moreover, a network security system prevents a variety of potential threats from entering or spreading within a network, thereby protecting a company's infrastructure from damage. This is a broad and comprehensive term that refers to processes, regulations, and settings pertaining to network use, accessibility, and overall threat prevention, as well as hardware and software solutions. It is the field of cybersecurity that focuses on protecting computer networks against cyber threats. To represent and solve the given problem, we establish the new mathematical concept known as interval-valued complex spherical fuzzy relations, defined as the cartesian product of two interval-valued complex spherical fuzzy sets. Furthermore, a range of interval-valued complex spherical fuzzy relations has been developed, characterized by interesting properties and outcomes. The interval-valued complex spherical fuzzy set and interval-valued complex spherical fuzzy relations supersede all pre-existing frameworks and methods for dealing with fuzziness. Additionally, this research investigates the application of interval-valued complex spherical fuzzy relations to assess the impact of various communication network security measures and the threats encountered by these networks. We further examine the positive, neutral, and negative effects of one factor on the other factors in the proposed applications, denoted by the membership grade, abstinence grade, and non-membership grade, respectively. Finally, we examine the proposed method to reveal its advantages and superiority to the current approaches.