𝒥⃗𝜌 neutrosophic Δϝ theory in mobile ad hoc network

Abstract

Applications of algebraic theory can be found in different logical fields, including materials science, hereditary qualities, design, as well as in hypothetical and applied math, including logarithmic calculation, cryptography, game hypothesis, and analysis of symphonies. Generally, binary operations are utilized to characterize the algebraic structure of a nonempty set. Group is a fundamental algebraic structure that frames the establishment of different structures in algebra. Further, the concept of a group has produced a lot of good ideas, such as subgroups, quotient groups, and simple groups, to divide larger groups into more understandable parts. Neutrosophic set is not only used in groups, but it is also applied in computing, network systems, processing systems, and computer technology. Neutrosophic logic is adopted in mobile ad hoc network (MANET). A mobile ad hoc network (MANET) is a wireless ad hoc network, and is often a self-configuring net of mobile devices with no requirement for added infrastructure. Further, we discuss the anti-fuzzy (Δϝ) subgroup. A Δϝ subgroup means a fuzzy subdivision of a category if the degree of membership of the combination of two components is larger than or equal to the minimum of their separate degrees. Moreover, in this study, we have examined the concepts of a implication-based (𝒥⃗𝜌) neutrosophic Δϝ subgroup ⱺⱱꬲꞧ а finite group and a 𝒥⃗𝜌 neutrosophic Δϝ normal subgroup ⱺⱱꬲꞧ а finite group. Finally, we demonstrate some of its fundamental properties.

Keywords

• 𝒥⃗𝜌 fuzzy subgroup
• 𝒥⃗𝜌- δϝ subgroup
• 𝒥⃗𝜌 neutrosophic δϝ subgroup
• 𝒥⃗𝜌 neutrosophic δϝ normal subgroup
• neutrosophic sets in mobile ad hoc network