The formal concept of lattice plays a vital role in knowledge discovery. Reduction of the attribute has many applications in machine learning technology and data mining fields. In this paper, we ...introduce an object ranking concept to define a consistency set and the reduction of the attributes by structural features. An incomplete information system works on the three-way concepts using the SE-ISI Context. The granular was emphasized with join (meet) irreducible sets using the object ranking concepts. A dual operator is defined based on the object ranking concepts and its properties and conditions are verified. Hence, this elaborates on the four kinds of reduction of the attributes. The ordered pairs give the knowledge of the attributes that deal with the interval set of both the approximation of rough set theory concerning the objects. Therefore, the relationship between four kinds of reduction of the attribute was appropriate to access the consistency set using the object ranking concepts by some of the theorems and examples.
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic ...behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
There are many applications of graph theory to a wide variety of subjects which include operation Research, Physics, chemistry, Economics, Genetics, Engineering, computer Science etc.,In a classical ...graph for each vertex or edge there are two possibilities arises that is either in the graph or not in the graph and this will not classical graph model for uncertain problems. Fuzzy set is a generalized version of the classical set in which objects have different membership degrees between zero and one. More work has already been done on fuzzy graphs. Zadeh introduced the degree of membership/Truth(T) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non-memebership/Falsehood(F) in 1983 and defined the intuitionstic fuzzy set. Smarandache introduced the degree of Indeterminancy/Neutrality(I) as an independent component in 1995 and defined the neutrosophic set on there compenents (T,I,F). Smarandache has introduced in 2020 the n-SuperHyperGraph, with super-vertices that are groups of vertices and hyper-edges defined on power-set of power-set... that is the most general form of graph as today, and n-HyperAlgebra. A SuperHyperGraph, is a HyperGraph (where a group of Edges form a HyperEdge) such that a group of vertices are united all together into a SuperVertex like a group of people (=vertices) that are united all together into an organization (=SuperVertex) ;and further on the n-SuperHyperGraph where many groups (=SuperVertices) are united all together to form a group-of-groups (called 2-SuperVertex, or Type-2 SuperVertex ), then a group of Type-2 SuperVertices forms a Type-3 SuperVertex, . . . , and so on up to Type-n SuperVertex, for any n 1, which better reflects our reality. Later Narmada Devi worked on new type of neutrosophic over,off graph and minimal domination via neutrosophic over graph and neutrosophic over topologized graph. A lot of topological indices are available in chemical-graph theory and H. Wiener proposed the first index to estimate the boiling point of alkanes called ‘Wiener index’. Many topological indices exist only in the crisp but it’s new to the Nover graph environment. The main aim of this paper is to define the topological indices in Nover graphs.
In this paper introduce the homomorphism, isomorphism, weak isomorphism and co-weak isomorphism of Neutrosophic over topologized graphs. Some properties of isomorphism are introduced. The isomorphism ...of Neu trosophic over topologized graphs equivalnce relation, weak isomorphism of Neutrosophic over topologized graphs partial order relation and complement of Neutrosophic over topologized graphs also derived here.
In this paper, the concepts of a neutrosophic τ -structure ring spaces, neutrosophic τ -structure ring GδT1/2 spaces and neutrosophic τ -structure ring exterior B spaces and neutrosophic τ -structure ...ring exterior V spaces are introduced. Some interesting functions that preserve neutrosophic τ -structure ring exterior B spaces and neutrosophic τ -structure ring exterior V spaces in the context of image and preimage are derived with the necessary examples.
In this paper, the new concept Topologized domination on Neutrosophic Graphs is introduced. The idea of N-Top domination is discussed in cycle, path, complete graph, star graph. The basic properties ...of N-Top dom set, N-Top minimum dom set, N-Top minimal dom set are introduced and N-Top dom number is also established with some necessary examples.
Neutrosophic over set can deal with the uncertainties related to the information of any decision making problem in real life scenaries, where fuzzy set may fail to handle those uncertainties ...properly. The study on presented in this “Neutrosophic Over topologized domination graphs” and also classification in different frame are discussed.The idea of NOver T op-dom set, NOver T op-minimum dom set, NOver T op-minimal dom set and NOver T op-dom number are introduced and necessary examples are established. In any neutrosophic over decision-making problem, the decision maker use the comparision of neutrosophic over number to choose alternative solutions.
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