ASPG

Neutrosophic Discrete Facility Location Problems

Hajem Ati Daham

Discrete facility location problems are classified as types of facility location problems, wherein decisions on choosing facilities in specific locations are made to serve the demand points of customers, thus minimizing the total cost. The covering- and median-based problems are the common classified types of discrete facility location problems, which both comprise different classes of discrete problems as reviewed in this research. However, the discrete facility location problems shown in deterministic and known information and data under uncertain, vague, and ambiguous environments have usually been solved using intuitionistic fuzzy approaches. Neutrosophic is recently applied to tackle the uncertainty and ambiguity of information and data. This paper considered solving the discrete facility location problems under the neutrosophic environment, wherein the information of the locations, distances, times, and costs is uncertain. The mathematical models for the main types of neutrosophic discrete facility location problems, which remain unclear till now despite previous related works, are formulated in this study. Numerical examples demonstrated testing of the neutrosophic discrete models and comparison with the optimization solutions obtained from the normal situations. 

Vol. 19 Issue. 1 PP. 29-47, (2022)

Time Q-Neutrosophic Soft Expert Set

Sumyyah Al-Hijjawi , Abd Ghafur Ahmad , Shawkat Alkhazaleh

This paper is a combination of time neutrosophic soft sets and Q- neutrosophic soft expert sets. We define the general concept of time Q-neutrosophic soft expert sets and study its properties. Some operations such as complement, union, and intersection are explored. Then a hypothetical application of this concept in the decision-making problem is given.

Vol. 19 Issue. 1 PP. 08-28, (2022)

Review of Generalized Neutrosophic Soft Set in Solving Multiple Expert Decision Making Problems

Sonali Priyadarsini , Ajay V. Singh , Said Broumi

To manage issues with incompleteness, indeterminacy, and awareness of inconsistent information, Maji presented the idea of a neutrosophic soft set by merging the ideas of a neutrosophic set and a soft set. The generalized neutrosophic soft set (GNSS) is an extension of this idea, which has now been developed further. At the beginning of this paper, we describe the definition of a generalized neutrosophic soft set. Then, we focus on the concepts of GNSS operations, such as AND, OR, complement, intersection, and union, and provide illustrated examples to describe a number of associated properties. Finally, a description of an algorithm and an application that uses GNSS to address challenges that arise when making decisions that need the experience of more than one specialist is offered here.

Vol. 19 Issue. 1 PP. 48-59, (2022)

Application of MBJ - Neutrosophic Set on Filters of Incline Algebra

Surya M. , P. Muralikrishna

The concept of fuzzy set has been generalized to many kinds and one among them is neutrosophic set which is a developed from intuitionistic fuzzy set by adding a components called indeterminate function between truth and falsity membership function. This neutrosophic set also moved a step forward and shows a variation in indeterminate function alone as an interval valued indeterminate function and other functions remains same and this is named as MBJ - neutrosophic set. Here, this work on the MBJ - neutrosophic set merged with incline algbera and introduces the idea of MBJ - neutrosophic filter of an incline algebraic structure and is engrossing with several results. Also, the level, cartesian product, projection, characteristic function and chain conditions are also disputed.

Vol. 19 Issue. 1 PP. 60-67, (2022)

Towards Smart Education in IoT and IoB Environment using the Neutrosophic Approach

Ossama H. Embarak , Fatima R. Aldarmaki , Maryam J. Almesmari

Due to the explosive growth of information in recent years, the function of education, which disseminates information, has become more important. Meanwhile, the paradigm of the educational process is undergoing a transformation to accommodate the many methods in which today's pupils learn. As a result, we should promote a more technologically advanced school setting. It uses a variety of technologies for communication and information to engage pupils and meet their individual needs. Continuously observing and evaluating the condition and actions of various students using information from various sensors and data processing platforms for providing feedback on the process of learning might improve the quality of learning for students. The potential for the IoT to improve people's quality of life and the efficiency of businesses is enormous. The Internet of Things (IoT) and Internet of behavior (IoB) have the potential to provide a new ecosystem for application development while also facilitating expansions and enhancements to key utilities in a wide variety of domains by means of a widely dispersed local network of intelligent items. Students will learn more quickly, and instructors will be able to do their jobs more effectively when the notion of the Internet of Things is used in any educational setting. The purpose of this article is to employ neutrosophic sets to demonstrate some of the most fundamental aspects of the Internet of Things. We used the MCDM methodology to evaluate the conflicting criteria, so we used the neutrosophic AHP method to compute the weights of the criteria, and then we used the neutrosophic VIKOR to rank the alternatives. We also demonstrated how IoT may help us make better choices in our everyday lives and contribute to a more intelligent educational system.

Vol. 19 Issue. 1 PP. 82-98, (2022)

Some remarks on ∆m (Iλ )-summability on neutrosophic normed spaces

Archana Sharma , Sajid Murtaza , Vijay Kumar

In the present paper, we use the difference operator ∆m (Iλ )-summability to define some new summability concepts on neutrosophic normed spaces. We also introduce concepts of generalized limit point, and cluster point and obtain some relationships among these notions. Finally, we define generalized Cauchy sequences on these spaces and present a characterization of a new summability method that preserves linear operators on neutrosophic normed spaces.

Vol. 19 Issue. 1 PP. 68-81, (2022)

On Neutrosophic Generalized Alpha Generalized Separation Axioms

Murtadha M. Abdulkadhim , Qays H. Imran , Amer K. Abed , Said Broumi

The paper provided a new notion of neutrosophic separation axioms as neutrosophic gαg-Ri-space & neutrosophic gαg-Tj-space (note that the indexes i & j are natural numbers of the spaces R & T are from 0 to 1 & from 0 to 2 alternately).

Vol. 19 Issue. 1 PP. 99-106, (2022)

On Neutrosophic Crisp Generalized Alpha Generalized Closed Sets

Murtadha M. Abdulkadhim , Qays H. Imran , Ali H. M. Al-Obaidi , Said Broumi

This study reveals new concepts of neutrosophic crisp closed sets named neutrosophic crisp g-closed sets, neutrosophic crisp αg-closed sets, neutrosophic crisp gα-closed sets, and neutrosophic crisp gαg-closed sets. Furthermore, their ultimate features in neutrosophic crisp topological spaces are examined. Moreover, the consequent new concepts are introduced, such as neutrosophic crisp gαg-closure and neutrosophic crisp gαg-interior and finding some of their characteristics.  

Vol. 19 Issue. 1 PP. 107-115, (2022)

Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version)

Florentin Smarandache

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses).

Vol. 19 Issue. 1 PP. 148-165, (2022)

Interval Valued Neutrosophic Subbisemirings of Bisemirings

M. Palanikumar , K. Arulmozhi , Aiyared Iampan

We introduce the notion of interval valued neutrosophic subbisemirings (IVNSBSs), level sets of IVNSBSs and interval valued neutrosophic normal subbisemirings (IVNNSBSs) of bisemirings. Also, we introduce an approach to (α , β)-IVNSBSs and IVNNSBSs over bisemirings. Let Ã be an interval valued neutrosophic set (IVN set) in a bisemiring S. We have proved that &scaron; = (sTA&sbquo; sIA&sbquo; sFA) is an IVNSBS of S if and only if all non-void level set S(T,S) is a subbisemiring of S for t, s ∈ [[0,1]].  Let Ã be an IVNSBS  of a bisemiring S and V be the strongest interval valued neutrosophic relation (SIVNR) of S.  Prove that Ã is an IVNSBS of S if and only if  V is an IVNSBS of S  X S. We illustrate homomorphic image of IVNSBS is an IVNSBS. We find that homomorphic preimage of IVNSBS is an IVNSBS. Examples are provided to illustrate our results.

Vol. 19 Issue. 1 PP. 116-131, (2022)

Agriculture Production Decision Making using Generalized q-Rung Neutrosophic Soft Set Method

G. Shanmugam , M. Palanikumar , K. Arulmozhi , Aiyared Iampan , Said Broumi

This paper introduces the generalized q-rung neutrosophic soft set (GqRNSSS) theory and its use to solve actual problems. We also define a few operations that make use of the GqRNSSS. The GqRNSSS is constructed by generalizing both the Pythagorean neutrosophic soft set (PyNSSS) and Pythagorean fuzzy soft set (PyFSS). We give a method for agricultural output that is based on the proposed similarity measure of GqRNSSS. If two GqRNSSS are compared, it can be determined whether or not a person produces good agricultural output. We support a strategy for dealing with the decision-making (DM) problem that makes use of the generalized qrung soft set model. In this article, we discuss the application of a similarity measure between two GqRNSSS in agricultural output. Show how they can be successfully applied to challenges with uncertainty.

Vol. 19 Issue. 1 PP. 166-176, (2022)

Neutrosophic C-Means Clustering with Optimal Machine Learning Enabled Skin Lesion Segmentation and Classification

Fatma Taher , Ahmed Abdelaziz

Early detection and classification of skin lesions using dermoscopic images have attracted significant attention in the healthcare sector. Automated skin lesion segmentation becomes tedious owing to the presence of artifacts like hair, skin line, etc. Earlier works have developed skin lesion detection models using clustering approaches. The advances in neutrosophic set (NS) models can be applied to derive effective clustering models for skin lesion segmentation. At the same time, artificial intelligence (AI) tools can be developed for the identification and categorization of skin cancer using dermoscopic images. This article introduces a Neutrosophic C-Means Clustering with Optimal Machine Learning Enabled Skin Lesion Segmentation and Classification (NCCOML-SKSC) model. The proposed NCCOML-SKSC model derives a NCC-based segmentation approach to segment the dermoscopic images. Besides, the AlexNet model is exploited to generate a feature vector. In the final stage, the optimal multilayer perceptron (MLP) model is utilized for the classification process in which the MLP parameters are chosen by the use of a whale optimization algorithm (WOA). A detailed experimental analysis of the NCCOML-SKSC model using a benchmark dataset is performed and the results highlighted the supremacy of the NCCOML-SKSC model over the recent approaches.

Vol. 19 Issue. 1 PP. 177-187, (2022)

Neutrosophic-Based Multi-Objectives Model for Financial Risk Management

Noura Metawa , Nahia Mourad

Financial organizations can no longer ignore the problem of managing risk. As a component of the financial system, efficient Financial Risk Management (FRM) may significantly affect business results. These findings show that the triangular neutrosophic numbers simulate capital asset key metrics. Performance metrics for capital assets may be modeled using this kind of value by accounting for all conceivable outcomes for their attainment. The profit on capital instruments, the risk of financial investments, and the covariance of capital instruments are the Key Performance Metrics (KPIs) modeled using triangular neutrosophic values. Specifically, this research employs two techniques. Prioritizing parameters for financial risk management dimensions using the Analytic Hierarchy Process (AHP). Second, the performance evaluation of financial risk management was evaluated from the perspective of several groups of specialists by the COCOSO method to assess the ranking of possible replies further. By using the presented method, we may better identify where to put our efforts and how to allocate our resources for greater effectiveness in managing financial risks.

Vol. 19 Issue. 1 PP. 188-199, (2022)

Apply Neutrosophic AHP Analysis of the Internet of Things (IoT) and the Internet of Behavior (IoB) in Smart Education

Ossama H. Embarak , Maryam J. Almesmari , Fatima R. Aldarmaki

The concept of the "Internet of Things" (IoT) has emerged in recent years to describe our increasingly interconnected physical world. Even if there are now goods on the market that are connected to the Internet of Things, there are still obstacles to be addressed, such as security concerns and a general lack of trust in and familiarity with the technology. The purpose of this research is to examine what goes into making a good Internet of Things (IoT) system for smart education that deals with IoT. In this research, we use neutrosophic theory and the Analytic Hierarchy Process (AHP) to create a decision-support system based on rules for assessing the impactful elements of the Internet of Things in smart education. According to the results of this investigation, security, value, and connectivity are more crucial than intangible qualities (Telepresence and Intelligence). This research suggests that the internet of behavior (IoB) and a sustainable Internet of Things (IoT) ecosystem requires strong IoT security measures to be implemented once smart education has established a reliable IoT connection. Likewise, smart education needs to think about the benefits of IoT security and IoT ethics for the goods they use and the comfort of their staff.

Vol. 19 Issue. 1 PP. 200-211, (2022)

Exact Solution for Neutrosophic System of Ordinary Differential Equations by Neutrosophic Thick Function Using Laplace Transform

George A. Toma

In this work, the idea of neutrosophic thick function has been proposed for solving a neutrosophic system of ordinary differential equations of various orders by the Laplace transform. This proposed scheme method is effective and simple to reach an exact solution.

Vol. 19 Issue. 1 PP. 212-216, (2022)

Neutrosophic Borda method

T. Witczak

In this paper we introduce and then study the general concept of neutrosophic Borda method. The idea is to combine Borda count (in one of its most typical versions) with neutrosophic sets (which allow us to deal with uncertainty in a very broad sense). We show the whole algorithm which is then illustrated with some numerical examples. Finally, we discuss several possible extensions of the proposed method. For example, we present neutrosophic approach to the problem of weights.

Vol. 19 Issue. 1 PP. 242-249, (2022)

Neutrosophic Statistics for Social Science

E. H. Marcia Esther , F. H. Robert Alcides , P. P. Rene Estalin

Social Science deals with the study of phenomena related to the social status of human beings. The importance of such sciences lies in the fact that they make it possible to know, predict, modify and improve the functioning of human societies today. Due to the great complexity of modern societies, it is virtually impossible to have accurate data or knowledge about any contemporary society. That is why neutrosophic theory is suitable for representing and modeling the data from studies on any social sciences. They may contain data that is contradictory, incomplete, inaccurate, vague, and so on. In particular, neutrosophic statistics generalizes classical statistics to interval-valued data. Since classical statistics are of great importance for the study of Social Sciences. We will emphasize the Legal Sciences in our approach

Vol. 19 Issue. 1 PP. 250-259, (2022)

Neutrosophic Image Segmentation: An Approach for the Treatment of Uncertainty in Multimodal Information Systems

Mohd A. Wajid , Aasim Zafar

Information explosion in this era has led to the proliferation of digital data in form of images, text, video, and audio. Uncertainty is a major issue in information access and retrieval models, and incomplete information needs to be treated in information systems because imprecision indicates the existence of a value that cannot be measured. There is no denial of the fact that uncertainty puts a hindrance in obtaining information in real-time systems, and as per knowledge rarely does any study of information retrieval using image segmentation treat imprecise and inconsistent information inherited in information systems. This work proposes to transform images in the neutrosophic domain for the treatment of uncertainty that persists in information recovery. Later, the image is segmented using the neutrosophic segmentation algorithm and its results are compared with the Modified Fuzzy c-Means segmentation algorithm, which is the earlier used segmentation algorithm in information systems. The experiment is conducted on a variety of multimodal images from the Berkeley Segmentation Dataset and Benchmark, showing the effectiveness of the proposed method for information systems. The proposed image segmentation using neutrosophy seems to yield a smaller error of 0.011, but the error obtained using the fuzzy c-means (MFCM) method is 0.13, which is larger than the proposed approach. The work also demonstrates how well neutrosophic segmentation can segment images having different noise levels as well as clean images. The results show that the proposed algorithm yields the most accurate segmented image for feature extraction which can be utilized while designing effective information systems.

Vol. 19 Issue. 1 PP. 217-230, (2022)

Neutrosophic Nano M Open Sets

A. Vadivel , C. John Sundar , Saraswathi , Tamilselvan

In this paper, we introduce the concepts of neutrosophic nano M-open sets and some stronger and weaker forms of neutrosophic nano open sets in neutrosophic nano topological spaces. Further, we dealt with the concepts of neutrosophic nano M-interior and M-closure operators. Moreover, we define the product related neutrosophic nano topological spaces and proved some theorems related to this.

Vol. 19 Issue. 1 PP. 132-147, (2022)

Analyzing the impact of social factors on homelessness with neutrosophic cognitive maps

D. C. Marcelo Raúl , T.T. Diego Fabricio , D. P. F. Patty Elizabeth

Homeless people are marginalized because they lack the resources necessary to participate in mainstream culture. It is not unusual to come across homeless persons in the streets of Quito, Ecuador, particularly in the downtown area. Society often refers to them as the unaccepted, the outcasts, the marginalized, and the homeless. Being a victim of aggressiveness is not an inevitable part of life on the streets. Still, unfortunately, we are seeing more and more instances of it being shown nearly every day. Many groups work to alleviate this problem by providing aid or enhancing the quality of life for these individuals. The goal of this study is to aid in strengthening the work of such institutions by providing a rationale for why so many crimes are decided to commit even against the homeless and how these institutions can better equip themselves to deal with the issue, as well as by providing tasks to assist direct the Homeless toward the Good Having to live Plan. A  cognitive map of neutrosophic causes and effects was constructed.

Vol. 19 Issue. 1 PP. 260-266, (2022)

On The Neutrosophic Formula of Some Matrix Equations Derived from Data Mining Theory and Control Systems

S. Obaid Jameel , A. Mahdi Salih , R. Adnan Jaleel , Musaddak M. A. Zahra

This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work.

Vol. 19 Issue. 1 PP. 267-271, (2022)

Neutrosophic K-means for market segmentation

A. Romero Fernández , G. Alvarez Gómez , C. Gómez Armijos

Markets may be broken down into subsets with the use of cluster analysis. Multivariate analytic methods are often used in traditional research. Due to their success in engineering, artificial neural systems have recently found use in business as well. When it comes to grouping observations with comparable traits or attributes, the K-means method is a common choice. It has various uses in marketing, but it finds particular success in cluster analyses of customer behavior. Several commercial packages include implementations of the K-means algorithm. Data mining statistical approaches like K-Means are useful for handling this data and analyzing it later on. For better results, this study combines the traditional K-Means technique with Neutrosophy, which accounts for the uncertainty inherent in such complicated data sets by factoring in the data's diversity and its inherent volatility as a result of proximity between the bounds of the separate segments as well as the members who make up each.

Vol. 19 Issue. 1 PP. 272-279, (2022)

Evaluation of Social Projects Using Neutrosophic AHP

R. Comas Rodríguez , J. M. D. Oca Sánchez , V. Lucero Salcedo

Recently, industrialization has led to a worldwide rise in energy usage. Consequently, satisfying rising energy demands has assumed more significance. Fuel, gasoline, and nat gas are all finite resources, making it all the more important to discover sustainable energy alternatives. To fulfill the current need for energy, renewable resources play a significant role. Therefore, energy decisions and government policy are of paramount importance for nations. Energy policy and judgment challenges, such as the appraisal of energy projects, the choice among fuel sources, the location of power plants, and the determination of energy policy, are solved using a variety of technical, financial, ecological, and social factors. Multi-criterion decision-making (MCDM) methodologies may be used to assess energy policy decisions, one of the important challenges for governments. Some of the challenges associated with making energy-related decisions and formulating policies are choosing between various energy sources, assessing the relative merits of various energy supply techniques, formulating an energy strategy, and carrying it through. Various forms of fuel sources are taken into account in the much research that has been conducted on energy decision-making challenges. Because they take into account several, sometimes competing, criteria in their assessments of potential solutions, MCDM techniques have proven useful in the resolution of energy-related decision-making issues. By combining MCDM with the neutrosophic set theory (NST), which captures the inherent ambiguity of human judgment, we may get more nuanced, tangible, and practical outcomes. This work intends to provide a thorough analysis of the methodology and implementations of neutrosophic MCDM in the power industry, as well as to synthesize the current literature and the latest recent breakthroughs to help guide researchers in this area. The neutrosophic Analytic Hierarchy Process (AHP) method is used to compute the weights of each criterion of energy in a social project. This research shows that neutrosophic AHP, either on its own or in combination with another MCDM approach, is the most often used MCDM technique.

Vol. 19 Issue. 1 PP. 280-288, (2022)

Indeterminate Likert Scale in Social Sciences Research

M. M. Rosa Leonor , G. S. Manaces Easud , P. P. Luis Fernando

The Likert scale is by far the most popular psychometric tool for collecting data. The ordinal structure and confined style of the Likert scale make it prone to information misinterpretation and loss. Depending on the consumers' moods, replies in the real world are sometimes erratic, imprecise, and ill-defined. Neutrosophy (the study of the implementation of the provisions and indeterminacy) is utilized to accurately portray the answers. This work introduces a neutrosophic-informed, agnostic version of the Likert scale. Clustering users based on their comments is an efficient method of segmenting the population and marketing to them. In this research, we offer a clustering approach for responses received using arbitrary Likert scales. When dealing with real-world events, indeterminate Likert scales are superior in recording replies properly.

Vol. 19 Issue. 1 PP. 289-297, (2022)

International Journal of Neutrosophic Science

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