New Aspects of Neutrosuperhyper Algebra With Its Application

New Aspects of Neutrosuperhyper Algebra With Its Application

M. Lathamaheswari, S. Sudha, Said Broumi, Florentin Smarandache
DOI: 10.4018/978-1-6684-4740-6.ch002
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Abstract

Security system is the process of developing, adding, and testing security features within applications to prevent security vulnerabilities against threats such as unauthorized access and modification. The implementation of such secure message passing protocols and the best, most dependable computing algorithms are made possible by hyperideal architecture. In this chapter, the authors introduced the concepts of interval-valued neutrosophic hyperring and interval-valued neutrosophic hyperideal. The algebraic properties and structural characteristics of the interval-valued neutrosophic hyperring and hyperideals are examined and established. The proposed concept has been applied in debit and credit card number pattern creation. The conclusion of the current effort also includes recommendations for the future.
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Introduction

The grade of membership in fuzzy sets is often represented as a single real integer in the interval (0,1). The interval-valued fuzzy set model developed by Truksen was used to reduce the uncertainty in the fuzzy set model’s grade of membership. Atanassov first developed intuitionistic fuzzy sets, a generalization of fuzzy sets, in 1986. In Bordbar, Cristea, and Novak (2017), this model was the same as interval valued fuzzy sets. The type of information that frequently exists in real-world situations but cannot be handled by intuitionistic fuzzy sets is indeterminate information. To overcome these issue Smarandache created the concept of neutrosophic model. Each premise in neutrosophic logic has a degree of truth (T), an indeterminacy (I), and a falsity (F), where T, I, and F are standard or non-standard subsets of ]-0,1+[ as might be seen in (Smarandache, F., 2003,2015). Numerous neutrosophic structures, such as neutrosophic groups, neutrosophic rings, neutrosophic modules, neutrosophichypergoups, neutrosophichyperrings, neutrosophic loops, and many more, have been developed since the advent of this theory. (Marty, 1934) first proposed the hyperstructure idea in 1934. (Corsini, 1993) developed the notion of hyperring homomorphism as well as the concept of hyperring and its generic form. The term H𝜐-ring, H𝜐-subring, and left and right H𝜐-ideal of a H𝜐-ring were all created by (Vougiousklis, 1995) as expansions of the notions linked to hyperings that Corsini had previously introduced. The triple (R,+,∙) is a hyperring in general if and only if the hyperoperations “+” and “∙” are such that (R,+) is a hypergroup, (R,∙) is a semihypergroup, and “∙” is distributive with respect to “+”. In essence, these structures are rings with roughly modified axioms. Researchers in the field of algebraic hyperstructures have studied many conception of hyperrings. Krasner, for instance, invented a type of hyperring in (Krasner, 1983) in which “∙”is a binary operation and “+” is a hyperoperation.

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