International Journal of Neutrosophic Science

Neutrosophic set (NS) is generalization of Intuitionistic Fuzzy Set(IFS) and Fuzzy Set (FS) where  Neutrosophic Set(NS) is the collection of Membership, Non-Membership, Indeterminacy Membership of the constituent element. This paper includes the modified circle breaking techinque which is used to evaluate the Shortest Path Problem in which edge weight are protrayed in Single Valued Linear Heptagonal Neutrosophic Number (SVLHNN) and an numerical illustration is given for the efficiency of the given algorithm.

In this paper, we introduce a new type of fuzzy Neutrosophic set called n-Cylindrical fuzzy Neutrosophic set (n-CyFNS), with I as independent neutrosophic component. The n-CyFNS can be claimed as the largest extension of fuzzy sets. In n-CyFNS, the degree of positive, neutral and negative membership functions are satisfying the condition, 0≤ βA(x) ≤1 and 0≤ αA n(x) + γAn(x) ≤ 1, n>1, is an integer.  Also the distance between two n- CyFNS and its properties are also defined. Along with basic operations on n- CyFNSs, we put forward two concepts-Neutrosophic affinity degree & Neutrosophic similarity index which is used to compare and correlate n-CyFNSs respectively. A comparison is made in the n-CyFNS environment using the existing correlation measures to check its reliability.

The new media is a crucial ply role in the market. The new media growth rapidly in the market so, select consumers and companies for competition. So, the new media is a complex task for companies and firms. The new media retrieval contains much content such as image retrieval, audio and video retrieval. The new media retrieval contains many criteria, and each criterion contains sub-criteria. So, use an MCDM method for dealing with this problem. The new media retrieval system is analyzing under a neutrosophic environment. The Decision-making trial and evaluation laboratory (DEMATEL) integrated with single-valued neutrosophic. DEMATEL method used to show importance and impact criteria of new media retrieval for helping companies in market competition. An example is provided for showing calculations.       

To build a strong country, build strong teaching. But teaching surrounding multiple risks. So this paper aims to identify and assess risks in teaching. The assessment risks in sanda teaching is a critical task and contain multiple conflict criteria. So we use Multi-Criteria Decision Making (MCDM). In this paper, we use an Analytical Hierarchy Process (AHP) to rank and compute each criterion's weights. We use five main and twenty sub-criteria. These criteria were evaluated under a neutrosophic environment—an example provided to present the outcomes of the proposed model. 

Potential mechanisms for dealing with water resources are provided by water resource management (WRM). To determine agricultural water resources, a new multi-criteria water resource management approach was created in this work. The management of agricultural water resources has become a major issue in the current circumstances. To create this circumstance, a multi-criteria approach is required. We were able to address a real-world water resource management issue using the suggested multi-criteria decision-making technique. The neutrosophic TOPSIS environment has been taken into account in this decision-making dilemma. Summertime water demand is high, and towards the end of summer, when monsoon season arrives, water demand is low in the agricultural field. During the monsoon season, it is not uncommon for rain to fall just in parts. In agriculture, growing crops during the monsoon season was difficult at the time. As a result, the nature of the water shortage in this area is non-linear and unclear. Because of this, we suggested an MCDM technique for WRM issues in a neutrosophic TOPSIS -environment context.

The globe has been coping with the COVID-19 epidemic, eagerly awaiting the completion of the vaccine process. Despite the Internet of Things (IoT) and its effect on supply networks, the recent epidemic has brought unprecedented supply chain disruptions. To assess the relevance of these issues, we speak with leading specialists. A novel distance-based similarity metric based on neutrosophic set theory is being used in this research to examine IoT challenges in the supply chain. The proofs for each of the properties are provided straightforwardly.

Deciding is the most vital part in any situation or problem that we face in our real time atmosphere. It is the situation where we must decide on the available choices. We have introduced Dodecagonal Neutrosophic Number and its properties. The concept of max-min and min-max principle is applied to the problem that is taken. The concept of heavy ordered weighted averaging operator by assigning equal weights to the attributes and a solution is found for a MCDM problem.

In this work a Neutrosophic approach has been implemented to assess the severity of diabetic neuropathy. Vibratory Perception Threshold (VPT) data was acquired from 600 participants. The acquired data was utilised to obtain the various criteria to assess the severity of diabetic neuropathy which is a fatal consequence of Diabetes mellitus. A single valued Neutrosophic set was employed to assess and evaluate the given medical condition. Multi Criteria Decision Making (MCDM) was used to address the severity. The hybrid score accuracy function and the collective correlation of the decision matrices were calculated and were used to estimate the weights which ultimately aided in the ranking process. The results corroborated that Grade II neuropathy is the most severe condition and needs more conscientious diagnosis. 

The aim of this paper is to introduce the concept of heptapartitioned neutrosophic soft set and to study some of its basic properties. This kind of set can be considered as a significant extension of the idea of neutrosophic set. In general, our research is based on the earlier study presented by Radha and Stanis Arul Mary in 2021. However, we combine their initial definition with the inspiring notion of soft set (which has been established by Molodtsov in 1999). We examine algebraic operations on our sets. Then we show that the particular choose of exactly seven neutrosophic logical values has an interesting interpretation in terms of ancient Jaina logic (which has been developed centuries ago in India to deal with imprecise knowledge and the matter of paraconsistency). Moreover, we exhibit some other potential practical applications of our theoretical concept. For example, it can be applied in widely understood social sciences.

Energy of graphs plays a vital role in the field of application in energy. Neutrosophic over top graph theory is more efficient and accurate results than other existing methods. In this research study, we present concepts of Energy, Laplaican energy and Signless laplacian energy in Nover top graphs. Describe some of their properties, develop relationship among them and their application.

The concept of interval-valued neutrosophic sets (IVNSs) was first introduced by Wang et al. (Wang, H.; Smarandache, F.; Zhang, Y. Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory and applications in computing. Hexis, Phoenix, Ariz, USA, 2005.). In this paper, the concept of IVNSs to ideals of Hilbert algebras is introduced. The homomorphic inverse image of interval-valued neutrosophic ideals (IVN ideals) in Hilbert algebras is also studied and some related properties are investigated.

In this paper, we introduce the concepts of neutrosophic nano δ-open sets and some stronger and weaker forms of neutrosophic nano open sets in neutrosophic nano topological spaces. And, show that the set of all neutrosophic nano δ-open sets are also a neutrosophic nano topology, which is called the neutrosophic nano δ topology. Further, we dealt with the concepts of neutrosphic nano δ-interior and neutrosophic nano δ-closure operators. Moreover, we define the product related neutrosophic nano topological spaces and proved some theorems related to this.

Let X be a finite set having n elements. The formula for giving the number of topologies T(n) is still not obtained. If the number of elements n of a finite set is small, we can compute it by hand. However, the difficulty of finding the number of the topology increases when n becomes large. A topology describes how elements of a set are spatially related to each other, and the same set can have different topologies. Studying this particular area is also a highly valued part of the topology, and this is one of the fascinating and challenging research areas. Note that the explicit formula for finding the number of topologies is undetermined till now, and many researchers are researching this particular area. This paper is towards the formulae for finding the number of neutrosophic clopen topological spaces having two, three, four, and five open sets. In addition, some properties related to formulae are determined.

In this paper, we introduce a new set called Pythagorean neutrosophic beta-open set with this concept, and we introduce interior and closure of Pythagorean neutrosophic beta-open set in a Pythagorean neutrosophic topological spaces by utilizing beta-open set and we introduce the chii, ii, iiibeta-spaces and di, ii, iiibetaspaces from the pair of distinct points and we have derived the necessary and sufficient conditions by utilizing beta-open sets. We also go through some containment relations for interiors and closures of beta-open sets and studied some of their characteristics.

Our purpose in this paper, is to introduce some of new continuous functions, called fuzzy neutrosophic perfectly continuous, fuzzy neutrosophic almost perfectly continuous and fuzzy neutrosophic strongly continuous in the fuzzy neutrosophic topological spaces. We give some theorems, propositions and some necessary examples related to presented definitions. Then, we discuss the relations among the new defined functions.