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The empirical correlation system serves as a crucial tool for unveiling the linear interconnections between two variables. Its significance lies in providing a prominent approach to depict a straightforward relationship without explicitly indicating a causal link between the sets involved. In the current research, an innovative concept of correlations is introduced specifically for Neutrosophic Over Soft Sets (Nos-sets).This novel framework involves a meticulous examination of basic definitions and operations associated with Neutrosophic Over Soft Sets. Furthermore, the study extends to the introduction of a groundbreaking concept :a topological space integrated with Neutrosophic Over Soft Sets (Nos-sets). This addition aims to broaden the scope of understanding and application in mathematical contexts. The research does not merely establish theoretical foundations; it also explores various properties and theorems related to the introduced concepts. This is complemented by a series of numerical examples designed to provide clarity and facilitate a comprehensive grasp of the material. To demonstrate the practical application of these concepts, the research utilizes the correlation framework to present a numerical illustration. Specifically, it is applied to determine the top-performing student at GFC School for the academic year 2022-2023, showcasing the real-world relevance and applicability of the proposed methodologies.

Municipal solid waste management (MSWM) has emerged as a major issue in India due to the massive amounts of waste generated on a daily basis. Governments are focusing on establishing a proper waste management system, including a timeline for the installation of waste processing and disposal facilities to reduce waste. For this problem, waste to energy (WtE) technologies have been identified because of their ability to convert waste into green energy while minimizing associated issues. This research investigates the different kinds of WtE treatments based on various factors, namely eco-friendly, budget friendly, technical, and social aspects. The findings of this study revealed which WtE treatments are best suited for waste management systems that convert green energy. In this paper, we propose the best WtE treatment for India using the interval-valued pythagorean neutrosophic fuzzy set (PNFS). We employ the WASPAS-CRITIC method in the interval-valued pythagorean neutrosophic fuzzy environment for this WtE treatment problem. Finally, a numerical example and a comparison are provided to illustrate the reliability and efficiency of the proposed technique.

Gold ornaments are always been seen as a metal of pride and happiness. It is also considered to be one of the auspicious costliest metals. Gold rate is found at an increasing rate from an early period. This paper analyzes the gold rate at six different cities in India. For each of the cities, neutrosophic mean and coefficient of variation have been calculated. The analysis results have been presented. In addition to that the neutrosophic analysis based on each month also has been calculated. The results help to know the beneficial month and city for the purchase of gold.

The degree of data uncertainty may be measured using a variety of mathematical techniques, but neutrosophic logic is a potent instrument for analysis when compared to fuzzy and intuitionistic fuzzy logics. This article introduces the novel idea of "dominance in neutrosophic over graph (NOG)s" and discusses some of the intriguing characteristics of complete, complete bipartite, and neutrosophic over bridge domination. With the relevant instances, the characterization of neutrosophic over domination set and neutrosophic over minimal domination set is developed, and their dominance numbers are examined.

This paper examines the asymptotic mean square solidness of a turbulent synchronization to time de lay neutrosophic stochastic framework. The Lyapunov solidness hypothesis is utilized to plan a neutrosophic-based stochastic framework with time postpone that is supposed to be asymptotically mean square steady. The Takagi Sugeno neutrosophic model had been made to make a neutrosophic spectator with a versatile refreshing system, as well as a neutrosophic spectator inside that presence. To communicate versatile update rules and control execution, direct framework disparity is utilized (LMI). A neutrosophic-based versatile control plot is assessed utilizing the idea of obscure. however, fixed boundary frameworks. The Lyapunov dependability hypothesis is utilized to foster the effectiveness of stochastic time delay tumultuous frameworks. For mathematical calculation, the Genesio-Tesi tumul tuous framework is used. The neutrosophic fluffy framework yield is completed utilizing MATLAB. Hypothetical outcomes are approved by this recreation.

Municipal solid waste (MSW) development has increased on a global scale, posing significant socio economic and environmental challenges. Waste to energy conversion is strategic because it can determine the best waste-to-energy technology. Recognizing the significance of waste in energy selection, this research aims to select the best technology based on its eco-friendliness. A two-phase methodology is used for presenting a framework for waste to energy technology selection. The first phase involves the selection of criteria for this problem and the perspectives of decision makers. Ranking the selected criteria using a novel SWARA method, and ranking the technology of WtE with respect to selected criteria weights are obtained. In this paper, we investigate the WtE technology problem using the novel concept of the Pythagorean Neutrosophic fuzzy set (PNFS). This set is a hybrid of the Pythagorean and Neutrosophic fuzzy sets. In this paper, we propose the best WtE technology for India. We employ the MULTIMOORA method in the Pythagorean Neutrosophic fuzzy environment for this purpose. Sensitivity and comparison analyses are also performed to ensure the framework’s robustness. The findings of this study are useful in ranking the technology, and as a result, waste management can replicate the proposed framework for waste disposal for their new platform.

The pandemic situation created by COVID’19 is ridiculous. It has made even the blood relations hide themselves from the infected person. The whole world was stunned by this situation. This is because of the uncertainty in the way in which this disease is spread. As an advancement of this disease, a few other variants like delta, omicron etc. also got spread. It is essential to find a solution to this situation . The variants Omicron and Delta are taken into consideration here. Though both the vibrant colours look alike, the symptoms and prevention methods changes for each of these vibrants. This work aims to make a study of the parameters responsible for these variants. As a result of this study, the parameters involved in the spread of these diseases are identified, and the prevention parameters are concluded. The major benefit of this comparatively study is to identify the parameters that are inconclusive, applying the concepts of fuzzy cognitive maps and neutrosophic cognitive maps is applied to bring out the result.

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.

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.

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.

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.

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.

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.

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.

In this paper, the concept of NSR contra continuous function is introduced. Several types of contra continuous functions in NSR spaces are discussed. Some interesting properties of NSR contra strongly precontinuous function is established

In this paper, we introduce and study a new class of neutrosophic closed set called neutrosophic m-closed set. In this respect, we introduce the concepts of neutrosophic m-continuous, strongly neutrosophic m continuous, neutrosophic m-irresolute and present their basic properties.

In this paper we introduce the concept of a new class of an ordered neutrosophic bitopological spaces. Besides giving some interesting properties of these spaces. We also prove analogues of Uryshon’s lemma and Tietze extension theorem in an ordered neutrosophic bitopological spaces.

In this paper, we introduce the concept of neutrosophic Baire space and present some of its characterizations.