Ayah Salama Khaskia

In this paper we introduce a new type of classical set called the neutrosophic classical set. After given the fundamental definitions of neutrosophic classical set operations, we obtain several properties, and discussed the relationship between neutrosophic classical sets and others. Finally, we generalize the classical probability to the notion of neutrosophic probability. This kind of probability is necessary because it provides a better representation than classical probability to uncertain events. Possible applications to computer sciences are touched upon.

ABSTRCTIn recent times, Information and Communication Technology (ICT) hasbeen developed and widely spread around world. ICT is used in various sectorsand considered a basis in the emergence of some important technologies such asvirtual reality technology. Virtual Reality (VR) is a special technology as anadvanced technology connected to several fields, e.g. training, learning, science,engineering, medicine, military, etc. VR has great potentials which enabled toperform several phenomena and experiments. Hence, several scenarios havebecome available. The purpose of this study is to shed light on virtual realitytechnology and list a glimpse of common publications and studies involved.

The advancements of mobile devices, public networks and the Internet of creature huge amounts of complex data, both construct & unstructured are being captured in trust to allow organizations to produce better business decisions as data is now pivotal for an organizations success. These enormous amounts of data are referred to as Big Data, which enables a competitive advantage over rivals when processed and analyzed appropriately. However Big Data Analytics has a few concerns including Management of Data, Privacy & Security, getting optimal path for transport data, and Data Representation. However, the structure of network does not completely match transportation demand, i.e., there still exist a few bottlenecks in the network. This paper presents a new approach to get the optimal path of valuable data movement through a given network based on the knapsack problem. This paper will give value for each piece of data, it depends on the importance of this data (each piece of data defined by two arguments size and value), and the approach tries to find the optimal path from source to destination, a mathematical models are developed to adjust data flows between their shortest paths based on the 0 - 1 knapsack problem. We also take out computational experience using the commercial software Gurobi and a greedy algorithm (GA), respectively. The outcome indicates that the suggest models are active and workable. This paper introduced two different algorithms to study the shortest path problems: the first algorithm studies the shortest path problems when stochastic activates and activities does not depend on weights. The second algorithm studies the shortest path problems depends on weights.

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 recent decades, Information and Communication Technology (ICT) has been advanced and widely spread around the globe in addition to ICT revolution and technological advances are considered the major role in the evolution of modern age, which is called "Digital Transformation Age". Therefore, Electronic Technology (E-Technology) has become one of the most prominent approaches such as Electronic Learning (E-Learning), Electronic Training (E-Training), Mobile Learning (M-Learning), Virtual Lab (V-Lab), Virtual University, etc. E-Technology includes some features, for instance anyone, anywhere, anytime and reducing of geographical barriers. ETechnology is a great trend and influences many fields and sectors such as Learning, Training, Military, Navy, Aviation, Medicine, and Digital space. According to nature of usage, E-Technology can be used in positive or negative trends. E-Technology is considered as a valuable tool in providing several opportunities for learning and training processes for individuals and organizations, especially in critical issues. Finally, we give a quick overview of neutrosophic data and some recent applications.

Neutrosophy has been introduced by Smarandache [7, 8] as a new branch of philosophy. The purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental definitions of neutrosophic set operations, we obtain several properties, and discussed the relationship between neutrosophic sets and others. Finally, we extend the concepts of fuzzy topological space [4], and intuitionistic fuzzy topological space [5, 6] to the case of neutrosophic sets. Possible application to superstrings and space–time are touched upon.

In this paper we introduce definitions of generalized neutrosophic sets. After given the fundamental definitions of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuitionistic fuzzy topological space [5, 6], and fuzzy topological space [4] to the case of generalized neutrosophic sets. Possible application to GIS topology rules are touched upon.

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 introduce definitions of generalized neutrosophic sets. After given the fundamental definitions of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuitionistic fuzzy topological space [5, 6], and fuzzy topological space [4] to the case of generalized neutrosophic sets. Possible application to GIS topology rules are touched upon.

“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.

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 introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies in [9,11] , the important topological neutrosophic ideals has been given in [4]. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to fiind new neutrosophic topology from the original one in [8]. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon.

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache in [30, 31, 32] and Salama et al. in [4-29]. In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some classes of neutrosoph-ic crisp nearly open sets are investigated and some applications are given. Finally we generalize the crisp topological and intuitioistic studies to the notion of neutrosophic crisp set. Possible applications to GIS topological rules 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 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.

The question of how an individual firm's social and environmental performance impacts its firm risk has not been examined in any empirical UK research. Does a company that strives to attain good environmental performance decrease its market risk or is environmental performance just a disadvantageous cost that increases such risk levels for these firms? Answers to this question have important implications for the management of companies and the investment decisions of individuals and institutions. The purpose of this paper is to examine the relationship between corporate environmental performance and firm risk in the British context. Using the largest dataset assembled so far, with community and environmental responsibility (CER) rankings for all rated UK companies between 1994 and 2006, we show that a company's environmental performance is inversely related to its systematic financial risk. However, an increase of 1.0 in the CER score is associated with only a 0.028 reduction in its β

The question of how an individual firm's social and environmental performance impacts its firm risk has not been examined in any empirical UK research. Does a company that strives to attain good environmental performance decrease its market risk or is environmental performance just a disadvantageous cost that increases such risk levels for these firms? Answers to this question have important implications for the management of companies and the investment decisions of individuals and institutions. The purpose of this paper is to examine the relationship between corporate environmental performance and firm risk in the British context. Using the largest dataset assembled so far, with community and environmental responsibility (CER) rankings for all rated UK companies between 1994 and 2006, we show that a company's environmental performance is inversely related to its systematic financial risk. However, an increase of 1.0 in the CER score is associated with only a 0.028 reduction in its β.