Four-Way Turiyam based Characterization of Non-Euclidean Geometry

Abstract

Recently, a problem is addressed while dealing the data with Non-Euclidean Geometry and its characterization. The mathematician found negation of fifth postulates of Euclidean geometry easily and called as Non-Euclidean geometry. However Riemannian provided negation of second postulates also which still considered as Non-Euclidean. In this case the problem arises what will happen in case negation of other Euclid Postulates exists. Same time total total or partial negation of Euclid postulates fails as hybrid Geometry. It become more crucial in case the data is unknown, incomplete or exists beyond the three-way space as heteroclinic pattern. To understand this problem, the current paper tried to distinguish Euclidean, Non-Euclidean, Anti-Geometry, Neutrogeometry and Turiyam or Unknown geometry using the complement operator with an example.

Social network analysis by Turiyam graphs

“…Accordingly, we ranked the rest as 2nd, 3rd, 4th, 5th, 6th, 7th and 8th based on their values in this SN. In this way, the Turiyam set and its graphical representation provides an alternative way to deal with SN data sets [19][20][21][22].…”

“…The motive is to utilize the properties of Turiyam set in graph theory for its various applications like social networks [17,18]. The authors defined some types of Turiyam graphs as a complete Turiyam graph, a strong Turiyam graph, and a constant Turiyam graph motivated by current studies [18][19][20][21][22]. To achieve this goal, some basic notation and its mathematical extension is required [16,22].…”

“…In this case, the trust values are based on human consciousness and it can be described either as trust on social network via action (t) , uncertainty trust on social network (i) , negative trust (or always opposing trust) on social network (f ) or hidden trust which is beyond any type of action shown on social network (l) . In such a situation, the Turiyam graph is appropriate to examine SN based on four membership degrees where FG, IFG and SVNG fail [16,[19][20][21][22]. In this way, the current paper defines the degree, order and size of the Turiyam graph and derives their properties.…”