A. A. Salama

We present in this paper the neutrosophic randomized variables, which are a generalization of the classical random variables obtained from the application of the neutrosophic logic (a new nonclassical logic which was founded by the American philosopher and mathematical Florentin Smarandache, which he introduced as a generalization of fuzzy logic especially the intuitionistic fuzzy logic ) on classical random variables. The neutrosophic random variable is changed because of the randomization, the indeterminacy and the values it takes, which represent the possible results and the possible indeterminacy . Then we classify the neutrosophic randomized variables into two types of discrete and continuous neutrosophic random variables and we define the expected value and variance of the neutrosophic random variable then offer some illustrative examples.

In this paper, we present the Neutrosophic time series by studying the classical time series within the framework of the Neutrosophic logic.(Logic established by the American philosopher and mathematician Florentin Smarandache presented it as a generalization of fuzzy logic, especially intuitionistic fuzzy logic). As an extension of this, AA Salama presented the theory of Neutrosophic crisp sets as a generalization of crisp sets theory. This study enables us to deal with all the time series values whether it is specified or not specified, we present the linear model for the Neutrosophic time series, and we test the significant of its coefficient based on Student's distribution. We present an example in which we pave the Neutrosophic time series according to the linear model, test the significant of its coefficient, and show how to deal with the unspecified values of the time series. Then we present the logarithmic model of the …

“Neutrosophics Knowledge” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professional, in good English and Arabic, containing a brief review of a problem and obtained results. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.

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: Paper aims to use the programming codes in calculating the values of neutrosophic grades and their representation in proving the certainty and uncertainty associated with the data of navigational projects development in the Suez Canal, Egypt. Added to, we reach a more descriptive of the data in terms of certainty and uncertainty, and that is through the neutrosophic representation of both the total revenue and the revenues of the Suez Canal from the transit carriers and ships. Finally, we will present a study of the decision-making process regarding the better investment in the Suez Canal. Is it investing in the oil tankers or investing in cargo ships, as this is done based on neutrosophic data. This will be done by studying optimistic, pessimistic, and remorse entrances to the neutrosophic data, to see which oil tankers or cargo ships offer better returns to the Canal.

The newly identified Coronavirus pneumonia, subsequently termed COVID-19, is highly transmittable and pathogenic with no clinically approved antiviral drug or vaccine available for treatment. Technological developments like edge computing, fog computing, Internet of Things (IoT), and Big Data have gained importance due to their robustness and ability to provide diverse response characteristics based on target application. In this paper, we present a novel Health-Fog framework universal system to automatically assist the early diagnosis, treatment, and preventive of people with COVID-19 in an efficient manner. Achieving an empirical of the proposed framework which mix between deep learning and Neutrosophic classifiers in the task of classifying COVID-19. There are some proposed applications based on the proposed COVID-X framework such as smart mask, smart medical suit, safe spacer, and Medical Mobile Learning (MML) will be presented. Computer-aided diagnosis systems could assist in the early detection of COVID-19 abnormalities and help to monitor the progression of the disease, potentially reduce mortality rates

In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the neutrosophic set. Figure 3 presents our neutrosophic package capability to draw figures of presented neutrosophic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. neutrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False.

In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute the distances between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region. Keywords: Neutrosophic Crisp Points; Neutrosophic Crisp Relations; Neutrosophic Crisp Sets; Neutrosophic Crisp Continuous Function; Neutrosophic Crisp Compact Spaces; Neutrosophic Crisp Nearly Open Sets; Neutrosophic Crisp Ideals; Neutrosophic Crisp Filter; Neutrosophic Crisp Local Functions; Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals; Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity; Neutrosophic Topological Region; Neutrosophic Closed Set and Neutrosophic Continuous Function; Neutrosophic Hesitancy Degree; Neutrosophic Crisp Topological Space; Neutrosophic Database; Neutrosophic Logic Manipulation; Neutrosophic Spatial Region.

This paper is devoted for presenting new neutrosophic similarity measures between neutrosophic graphs. We propose two ways to determine the neutrosophic distance between neutrosophic vertex graphs. The two neutrosophic distances are based on the Haussdorff distance, and a robust modified variant of the Haussdorff distance, moreover we show that they both satisfy the metric distance measure axioms. Furthermore, a similarity measure between neutrosophic edge graphs, that is based on a probabilistic variant of Haussdorff distance, is introduced. The aim is to use those measures for the purpose of matching neutrosophic graphs whose structure can be described in the neutrosophic domain.

Recently designing an effective intrusion detection systems (IDS) within Mobile Ad Hoc Networks Security (MANETs) becomes a requirement because of the amount of indeterminacy and doubt exist in that environment. Neutrosophic system is a discipline that makes a mathematical formulation for the indeterminacy found in such complex situations. Neutrosophic rules compute with symbols instead of numeric values making a good base for symbolic reasoning. These symbols should be carefully designed as they form the propositions base for the neutrosophic rules (NR) in the IDS. Each attack is determined by membership, nonmembership, and indeterminacy degrees in neutrosophic system. This research proposes a MANETs attack inference by a hybrid framework of Self-Organized Features Maps (SOFM) and the genetic algorithms (GA). The hybrid utilizes the unsupervised learning capabilities of the SOFM to define the MANETs neutrosophic conditional variables. The neutrosophic variables along with the training data set are fed into the genetic algorithm to find the most fit neutrosophic rule set from a number of initial subattacks according to the fitness function. This method is designed to detect unknown attacks in MANETs. The simulation and experimental results are conducted on the KDD-99 network attacks data available in the UCI machine-learning repository for further processing in knowledge discovery. The experiments cleared the feasibility of the proposed hybrid by an average accuracy of 99.3608 % which is more accurate than other IDS found in literature.

In this paper, we aim to develop a new type of neutrosophic crisp set called the retract neutrosophic crisp set and shows a grayscale image in a 2D Cartesian domain with neutrosophic crisp components in the neutrosophic domain. The introduced set is a retraction of any triple structured crisp set. Whereas, the retract set deduced from any neutrosophic crisp set is coincide its corresponding star neutrosophic crisp set defined in by Salama et al. [1]. Hence we construct a new type of neutrosophic crisp topological spaces, called the retract neutrosophic crisp topological space as a retraction of the star neutrosophic topological space. Moreover, we investigate some of its properties.

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In neutrosophic set, indeterminacy is quantified explicitly and truth-membership, indeterminacy-membership and falsity-membership are independent. So it is natural to adopt for that purpose the value from the selected set with highest degree of truth-membership, indeterminacy membership and least degree of falsity-membership on the decision set. These factors indicate that a decision making process takes place in neutrosophic environment. In this paper, we introduce and study the probability of neutrosophic crisp sets. After given the fundamental definitions and operations, we obtain several properties and discussed the relationship between them. These notions can help researchers and make great use of it in the future in making algorithms to solving problems and manage between these notions to produce a new application or new algorithm of solving decision support problems. Possible applications to mathematical computer sciences are touched upon.

In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the nuetrosophic set. Figure 3 presents our neutrosphic package capability to draw figures of presented neutrosphic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. nuetrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False.

This paper is an attempt of proposing the processing approach of neutrosophic technique in image processing. As neutrosophic sets is a suitable tool to cope with imperfectly defined images, the properties, basic operations distance measure, entropy measures, of the neutrosophic sets method are presented here. İn this paper we, introduce the distances between neutrosophic sets: the Hamming distance, the normalized Hamming distance, the Euclidean distance and normalized Euclidean distance. We will extend the concepts of distances to the case of neutrosophic hesitancy degree. Entropy plays an important role in image processing. In our further considertions on entropy for neutrosophic sets the concept of cardinality of a neutrosophic set will also be useful. Possible applications to image processing are touched upon.

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images.