Journal of Neutrosophic and Fuzzy Systems

Recently, Turiyam set is introduced to deal with data set beyond three-way fuzzy space. In this process a problem is addressed while precise representation of Turiyam attributes in matrix format for knowledge processing tasks. To resolve this issue, current paper defines concept of symbolic Turiyam matrix by using the symbolic Turiyam set concept. In addition, the paper illustrates several examples to clarify the algebraic structure of these matrices such as addition, multiplication, and symmetry of these matrices.

This paper is dedicated to define for the first time the concept of Symbolic Turiyam vector space as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. Also, we illustrate many examples to show and clarify the validity of this work.

This paper is dedicated to present a wide review study on the recent advantages of neutrosophic linear diophantine equations and number theory.   We revise the neutrosophic linear diophantine equations, refined neutrosophic Diophantine equations, and n-refined neutrosophic linear Diophantine equations.

Neutrosophic Algebraic structures are rich fields for researchers to get many interesting generalizations of classical and fuzzy structures.  This Study is dedicated to give the interested reader some of special neutrosophic algebraic substructures of neutrosophic algebraic structures, especially AH-substructures in neutrosophic rings, spaces, modules, and their generalizations.

Recent time many researchers focused on dealing the uncertainty and its characterization. The precise approximation of uncertainty in many-valued data set is one of the major tasks. It becomes more difficult in case the given data sets are non-Euclidean. Hence the rough fuzzy set and its graphical visualization is introduced in this paper for knowledge processing tasks.

This paper solves the imperfect triplets problem in refined neutrosophic rings, where it presents the necessary and sufficient conditions for a triple  (x,y,z) to be an imperfect triplet in any refined neutrosophic ring. Also, this work introduces a full description of the structure of imperfect triplets in numerical refined neutrosophic rings such as refined neutrosophic ring of integers Z(I1,I2) , refined neutrosophic ring of rationales Q(I1,I2), and refined neutrosophic ring or real numbers  (R(I1,I2). 

This paper defines  the concept of kernel subgroup of an intuitionistic fuzzy group. Also, it proves that this kernel is a group in the ordinary algebraic meaning as a direct application of the concept of kernel in fuzzy and anti-fuzzy groups. Also, we derive some properties of intuitionistic fuzzy groups.

In this paper, we show that for a finite game with two players A , B: Each winning strategy of the first player A can be represented by a neutrosophic subgroup of the neutrosophic group ( , and each winning strategy of the second player B can be represented by an elementary abelian group .   Also, we introduce the concept of algebraically relative  games and present some examples on it.