In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.

In this paper, we define for the first time the concept of symbolic Turiyam ring as a direct application of Turiyam symbolic set and as a new generalization of neutrosophic rings. Also, we study many of essential properties and related concepts of these rings such as AH-ideals and subrings. On the other hand, we illustrate many examples to clarify the validity of our work.

Recently, Turiyam set is introduced for dealing the fourth dimensional data sets. These types of data sets exists when an expert unable to categorize them in Euclidean, Non-Euclidean, Hybrid or NeutroGeometry. To deal with these types of data set Turiyam matrix and its algebra is required. Hence the current paper introduce the concept of Symbolic Turiyam R-module as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. The paper also presents concept pf finite Turiyam modulo integer and illustrate many examples to show and clarify the validity of this work.

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.

A consecutive sample of 50 patients with a diagnosis of definite multiple sclerosis was evaluated by means of the Clinical Interview Schedule (CIS) and other psychopathological instruments. A global prevalence of psychopathology of 54% was found, with the prevalence of depression being 22%. Moreover, 46% of the sample presented signs indicative of neuropsychological deterioration in the Benton Visual Retention Test. The association between the presence of psychopathology and the social and neurological characteristics of the sample was also investigated, with results of low significance.