On Refined Neutrosophic R-module

Abstract

Modules are one of the fundamental and rich algebraic structure concerning some binary operations in the study of algebra. In this paper, some basic structures of refined neutrosophic R-modules and refined neutrosophic submodules in algebra are generalized. Some properties of refined neutrosophic R-modules and refined neutrosophic submodules are presented. More precisely, classical modules and refined neutrosophic rings are utilized. Consequently, refinedneutrosophic R- modules that are completely different from the classical modular in the structural properties are introduced. Also, neutrosophic R-module homomorphism is explained and some definitions and theorems are presented.

Some applications of Weak-multiplication modules in Neutrosophic set environment

“…Definition 2.4. [29] Let (R, +, •) be a ring and a neutrosophic set denoted by R and I. So Neutrosophic R = (R(I), +, •) is called a neutrosophic ring.…”

“…Definition 2.5. [29] Let (M, +, •) be a module over R. Then (M (I), +, •) is a weak neutrosophic module over R, and it is called a strong neutrosophic module if it is a module over R(I).…”

“…Abed et al [27,28] introduced some neutrosophic algebraic structures, and module theory and studied their properties and applications. Olgun and Bal [29] give some studies on neutrosophic module theory. Auad et al [30,31] introduced some results of best co-approximation specifications of co-proximal and co-Chebyshev of unbounded functions in weighted spaces.…”

Convergence of Neutrosophic Random Variables

“…The notion of neutrosophic logic is an extension of intuitionistic fuzzy logic by putting indeterminacy item (I) where I 2 = I, ..., I n = I, 0.I = 0; n ∈ N and I −1 is undened (see [23], [36]). Neutrosophic logic has plenty of applications in many areas of sciences including multicriteria decision making [33], [22], [29], machine learning [6], [31], intelligent disease diagnosis [34], [11], communication services [8], pattern recognition [32], social network analysis and e-learning systems [24], physics [38], sequences spaces [15] and many others. Neutrosophic logic has helped many multicretia decision-making problems eciently like nding credit rating, personal selection, among other.…”