Most complex problems in the real-world typically involve uncertain,incomplete and indeterminate two-dimensional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet the demand for models that has the ability to handle these information with these characteristics, the introduction of neutrosophic sets (NSs) was followed by their extension to the complex neutrosophic sets (CNSs). In this paper, we introduce the concept of Q- complex neutrosophic set (Q-CNS) by extending the ranges of the membership functions in Q-neutrosophic set (Q-NS) from [0,1] to the unit circle in the complex plane. Q-CNS plays a key role in the decision making theory, where the extra information provided by the elements of the Q-set serve in modeling of some decision making problems. Based on this new concept we define the basic theoretical operations such as complement, equality, subset, union, intersection, Q-complex neutrosophic product and Cartesian product. Some related examples are also given to enhance the understanding of the proposed concepts. The basic properties of these operators are also verified with supporting proofs.
Read MoreDoi: https://doi.org/10.54216/IJNS.200201
Vol. 20 Issue. 2 PP. 08-19, (2023)
This article presents the notion of n-refined neutrosophic modules such as cyclic, simple, and finitely generated modules. n-refined neutrosophic is a generalization of neutrosophic properties. This paper presents new relations among n-refined neutrosophic modules. Finally, several examples and properties have been studied about the relations between these modules.
Read MoreDoi: https://doi.org/10.54216/IJNS.200202
Vol. 20 Issue. 2 PP. 20-26, (2023)
The logistic distribution is widely used to model various types of applied data. The modified logistic distribution under neutrosophic statistics is introduced in this work. The neutrosophic logistic distribution (NLD) and its engineering applications are mainly emphasized. An appealing characteristic of the suggested NLD is that it is useful to many widely utilized survival assessment metrics, including the reliability function, hazard function, and survival function. Applications of some mathematical and statistical properties of the suggested model are discussed. Numerical investigations on simulated data are used to validate the theoretical findings experimentally. From an application point of view, it is inferred that the proposed distribution fits data with imprecise, hazy, and fuzzy information better than the usual model. In addition, the maximum likelihood (ML) technique for the proposed model is discussed under the neutrosophic inference framework. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems.
Read MoreDoi: https://doi.org/10.54216/IJNS.200203
Vol. 20 Issue. 2 PP. 27-39, (2023)
In this study, the research aims to use some methods that deal with several independent variables with a dependent variable, where two methods were used to deal with, which is the method of slice inverse regression (SIR), which is considered a non-classical method, and two methods of machine learning, which is (TLBO, PSO), which is most popular of the teaching methods machine learning, the work of (SIR), (TLBO, PSO) is based on making reduced linear combinations of a partial set of the original explanatory variables, which may suffer from the problem of heterogeneity and the problem of multicollinearity between most of the explanatory variables. These new combinations of linear compounds resulting from the two methods will reduce the largest number of explanatory variables to reach one or more new dimensions called the effective dimension. The root mean square error criterion will be used to compare the two methods to indicate the preference of the methods.
Read MoreDoi: https://doi.org/10.54216/IJNS.200204
Vol. 20 Issue. 2 PP. 40-54, (2023)
The term "Internet of Things" (IoT) refers to a network of connected, intelligent devices that are responsible for the collecting and dissemination of data. Because technology automates the tasks we do daily, our lives have become simpler as a result. However, with a typical architecture for the cloud and the Internet of Things, real-time data processing is not always practicable. This is particularly true for latency-sensitive apps. This eventually resulted in the development of fog computing. On the one hand, the fog layer may perform computations and data processing at the very edge of the network, which enables it to provide results more quickly. On the other hand, this pushes the attack surface closer to the machines themselves, which is a security risk. Because of this, the sensitive data that is stored on the layer is now susceptible to assaults. Therefore, considering the security of the fog-IoT is of the utmost significance. A system or platform's level of security is determined by a number of different elements. When it comes to conducting an accurate risk assessment, the sequence in which these considerations are considered is of the utmost importance. Because of this, determining the level of security offered by fog and IoT devices becomes a Multi-Criteria Decision-Making (MCDM) dilemma. This article presents a two-stage hybrid multi-criteria decision-making model that is based on type-2 neutrosophic numbers (T2NNs). The goal of this article is to give scientists and practitioners a decision-making tool that is both easy and versatile. The initial step of this process is determining the weights of criteria by the AHP method in the T2NN environment. Second, the T2NN-based Multi-Attributive Border Approximation area Comparison (MABAC) method is used to rank the various fog security based on IoT. Both of these methods are described in more detail below. With the help of the comparison study, the high reliability and robustness of the combined AHP and MABAC based type-2 neutrosophic model have been proven.
Read MoreDoi: https://doi.org/10.54216/IJNS.200205
Vol. 20 Issue. 2 PP. 55-76, (2023)
A lot of research has been done on the types of open and closed sets in general topological spaces and also in general bitopological spaces. Types of sets like pre-open sets and pre-closed sets, semi-open sets and semi-closed sets, Alpha-open sets, and Alpha-closed sets, regular open sets and regular closed sets, g-open sets and g-closed sets, and many more have been defined and studied. In the current study, an attempt has been made to define and give examples of a new category of open and closed sets, namely, NeutroOpen and NeutroClosed sets. Further, the concept of neutron-topology is used to define NeutroPreOpen and NeutroPreClosed sets, NeutroSemiOpen and NeutroSemiClosed sets, NeutroAlphaOpen and NeutroAlphaClosed sets, NeutroRegularOpen and NeutroRegularClosed sets, NeutroBetaOpen, and NeutroBetaClosed sets, and several examples have been given to illustrate each of the new classes of sets. Also, the concept of AntiTopology has been used to define another class of sets, namely, AntiOpen and AntiClosed sets of the above five classes of sets, namely, regular-open/closed; semi-open/closed, Alpha-open/closed, Beta-open/closed pre-open/closed sets. Further, a new class of subsets is identified which are named as NeutroTauOpen and NeutroTauClosed sets. Similar subsets in anti-topological spaces are named as AntiTauOpen and AntiTauClosed sets.
Read MoreDoi: https://doi.org/10.54216/IJNS.200206
Vol. 20 Issue. 2 PP. 77-85, (2023)
It is evident how crucial education is to a person's overall development. The knowledge of the economy and society is still in its infancy. In terms of social and economic elements, education has emerged as the most significant factor for individual and national growth. Given this context, it would be worthwhile to examine the New Education Policy 2020 for the benefits and impacts it has on the various stakeholders. Such analysis is important to fulfill the needs and objectives of NEP-2020. Despite having many universities and schools, Indian education still needs some improvements. Many Indian children still do not have access to education, and more importantly, the education system in India has not undergone significant reform in the last few decades, so changes must be made to keep up with the changing needs of society. The purpose of this study is to use the neutrosophic PESTEL analysis technique to mathematically identify and rank the major factors required to be identified for the successful implementation of NEP. Numerous factors that are grouped into six primary categories—political, economic, social, technological, legal, and environmental. These are presented by a thorough literature review of the subject. The present work employs neutrosophic PESTEL analysis, to identify the main obstacles to the implementation and execution of NEP-2020 in India. The study shows that social and economic factors, with 84% and 60% respectively play a significant role while political and technical factors are also important and come in second place since they each represent 25% and 34% of the barriers to the implementation of the NEP-2020. The last two factors are legal and environmental, contributing only 13% and 3%, respectively. The primary goal of the study is to identify and statistically rank the biggest obstacles to NEP-2020 implementation in India. In many aspects, this research will help government organizations and policymakers prioritize the main obstacles early in the implementation process as well as during execution, ensuring that the results are as anticipated and that the project is finished within the allotted time limit.
Read MoreDoi: https://doi.org/10.54216/IJNS.200207
Vol. 20 Issue. 2 PP. 86-106, (2023)
In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. First of all, we propose the concepts of Pythagorean fuzzy t-norm and t-conorm and show that some Pythagorean fuzzy t-norms and t-conorms are expressed via ordinary continuous Archimedean tnorms and t-conorms. Then we define the concepts of PFVNS and PFVNV and provide a tool to construct a PFVNV from an ordinary neutrosophic fuzzy value. We also define some set theoretic operations between PFVNSs and some algebraic operations between PFVNVs via t-norms and t-conorms. With the help of these algebraic operations we propose some weighted aggregation operators. To measure discrimination information of PFVNVs, we define a simplified neutrosophic valued modified fuzzy cross-entropy measure. Moreover, we introduce a multi-criteria decision making method in Pythagorean fuzzy valued neutrosophic environment and practice the proposed theory to a real life multi-criteria decision making problem. Finally, we study the comparison analysis and the time complexity of the proposed method.
Read MoreDoi: https://doi.org/10.54216/IJNS.200208
Vol. 20 Issue. 2 PP. 107-134, (2023)
When compared to its extension, hypersoft set, a soft set only deals with a single set of attributes, while a hypersoft set deals with several attribute-valued disjoint sets that correspond to various attributes. Several researchers have developed models based on soft sets, but the majority of these models suffer from limitations since they are inappropriate for interval-type data or uncertain data. In order to address these issues, a novel model interval-valued fuzzy hypersoft set (IV F HS -set) is presented in this research article. This model not only resolves the inadequacy of soft set for distinct attributes for non-overlapping attribute-valued sets, but also addresses the limitations of soft set-like models with having data in interval environment. This work modifies the current fuzzy hypersoft set concept and introduces certain fundamental ideas, such as subset, not set, whole set, and absolute relative null set, relative absolute set and aggregation operations e.g. intersection, union, extended intersection, restricted union, complement, OR, AND, difference, restricted difference are discussed under IV F HS -set environment with illustrated examples. Some new hybrids of fuzzy hypersoft set under interval-valued settings are also discussed. Moreover, some extensions of IV F HS -set are presented along with different operations.
Read MoreDoi: https://doi.org/10.54216/IJNS.200209
Vol. 20 Issue. 2 PP. 135-161, (2023)
Digital learning is a broad umbrella of any form of learning incorporating novel digital technology aspects in teaching and assessment to facilitate learning and engage students. Most education settings have moved from face–to–face to e-learning platforms worldwide ever since the beginning of the COVID-19 pandemic. Assessment of the efficiency of digital learning is essential, and assessment criteria may take several forms. Digital learning effectiveness assessment has received a significant amount of attention and work; nevertheless, a generalized quantitative evaluation model that considers the inter-affected link among criteria and the uncertainty of personal perception simultaneously is still absent. In this study, the hybrid MCDM model that was suggested handles the independent relations of assessment criteria with factor analysis, and it addresses the dependency relations of assessment via the use of AHP. The AHP and neutrosophic integral approaches are used for the purpose of creating synthetic usefulness in line with the environment of subjective perception. This quantitative research study explores students’ readiness to continue utilizing e-learning while measuring satisfaction levels with the e-learning system among higher education students in the Gulf area. Moreover, students’ behavior intention is measured here. Descriptive analysis was opted to achieve the aim of the study. Data analysis demonstrated that higher education students showed medium to high readiness levels towards e-learning and were identified with a medium level of satisfaction with the e-learning system. Moreover, students demonstrated a high intent to utilize the e-learning platform in case of offering parallel e-learning courses in the future.
Read MoreDoi: https://doi.org/10.54216/IJNS.200210
Vol. 20 Issue. 2 PP. 162-177, (2023)