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 defin itions 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], intuition istic fuzzy topological space [5,6], and fu zzy topological space [4] to the case of generalized neutrosophic sets. Possible applicat ion to GIS topology rules are touched upon.

Abstract-The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic crisp functions.

In this paper, we introduce and study the concepts of correlation and correlation coefficient of neutrosophic data in probability spaces. In the case of finite spaces, these results give the results due to Salama et al. [16, 17, 18] and study some of their properties.

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.

Cardiotocography is a medical device that monitors fetal heart rate and the uterine contraction during the period of pregnancy. It is used to diagnose and classify a fetus state by doctors who have challenges of uncertainty in data. The Rough Neural Network is one of the most common data mining techniques to classify medical data, as it is a good solution for the uncertainty challenge. This paper provides a simulation of Rough Neural Network in classifying cardiotocography dataset. The paper measures the accuracy rate and consumed time during the classification process. WEKA tool is used to analyse cardiotocography data with different algorithms (neural network, decision table, bagging, the nearest neighbour, decision stump and least square support vector machine algorithm). The comparison shows that the accuracy rates and time consumption of the proposed model are feasible and efficient.

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