International Journal of Neutrosophic Science

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Q-Complex Neutrosophic Set

Ashraf Al-Quran , Abd Ghafur Ahmad , Faisal Al-Sharqi , Abdalwali Lutfi

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.

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Vol. 20 Issue. 2 PP. 08-19, (2023)

n-Refined Indeterminacy of Some Modules

M. Abdallah Salih , D. Alawi Jarwan , M. Mohammed Abed

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.

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Vol. 20 Issue. 2 PP. 20-26, (2023)

A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling

A. M. Mohamed Ibrahim , Zahid Khan , Fuad S. Al-Duais

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.

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Vol. 20 Issue. 2 PP. 27-39, (2023)

Comparison Slice Inverse Regression Method with Machine Learning Techniques in Multivariate Data

Omar A. abd Alwahab

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.

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Vol. 20 Issue. 2 PP. 40-54, (2023)

An integrated AHP MCDM based Type-2 Neutrosophic Model for Assessing the Effect of Security in Fog-based IoT Framework

Mohammad D. Alshehri

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.

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Vol. 20 Issue. 2 PP. 55-76, (2023)

A new class of NeutroOpen, NeutroClosed, AntiOpen and AntiClosed sets in NeutroTopological and AntiTopological spaces

Jeevan K. Khaklary , G. Chandra Ray

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.

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Vol. 20 Issue. 2 PP. 77-85, (2023)