A Geometric Interpretation of the Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set

In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.Comment: 9 pages. Presented at the 2003 BISC FLINT-CIBI International Workshop on Soft Computing for Internet and Bioinformatics, University of Berkeley, California, December 15-19, 2003, under the title "Generalization of the Intuitionistic Fuzzy Set to the Neutrosophic Set

T-MBJ NEUTROSOPHIC SET UNDER M-SUBALGEBRA

In this paper, the idea of T-MBJ neutrosophic set is introduced in which MBJ-neutrosophic set is used to present this new set called T-MBJ neutrosophic set. furthermore the notion of T-MBJ neutrosophic M- subalgebra on G-algebra is also introduced and provide the conditions for T-MBJ neutrosophic M-subalgebra. The word M in the term M-subalgebra, represents the initial of author's rst name Mohsin. We study the T-MBJ neutrosophic set through dierent characteristics and also prove some results for better understanding of newly dene T-MBJ neutrosophic set

Quadruple Neutrosophic Theory And Applications Volume I

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Smarandache introduce for the first time the neutrosophic quadruple numbers (of the form + + + ) and the refined neutrosophic quadruple numbers

Certainty of outlier and boundary points processing in data mining

Data certainty is one of the issues in the real-world applications which is caused by unwanted noise in data. Recently, more attentions have been paid to overcome this problem. We proposed a new method based on neutrosophic set (NS) theory to detect boundary and outlier points as challenging points in clustering methods. Generally, firstly, a certainty value is assigned to data points based on the proposed definition in NS. Then, certainty set is presented for the proposed cost function in NS domain by considering a set of main clusters and noise cluster. After that, the proposed cost function is minimized by gradient descent method. Data points are clustered based on their membership degrees. Outlier points are assigned to noise cluster and boundary points are assigned to main clusters with almost same membership degrees. To show the effectiveness of the proposed method, two types of datasets including 3 datasets in Scatter type and 4 datasets in UCI type are used. Results demonstrate that the proposed cost function handles boundary and outlier points with more accurate membership degrees and outperforms existing state of the art clustering methods.Comment: Conference Paper, 6 page

A Convolutional Neural Network model based on Neutrosophy for Noisy Speech Recognition

Convolutional neural networks are sensitive to unknown noisy condition in the test phase and so their performance degrades for the noisy data classification task including noisy speech recognition. In this research, a new convolutional neural network (CNN) model with data uncertainty handling; referred as NCNN (Neutrosophic Convolutional Neural Network); is proposed for classification task. Here, speech signals are used as input data and their noise is modeled as uncertainty. In this task, using speech spectrogram, a definition of uncertainty is proposed in neutrosophic (NS) domain. Uncertainty is computed for each Time-frequency point of speech spectrogram as like a pixel. Therefore, uncertainty matrix with the same size of spectrogram is created in NS domain. In the next step, a two parallel paths CNN classification model is proposed. Speech spectrogram is used as input of the first path and uncertainty matrix for the second path. The outputs of two paths are combined to compute the final output of the classifier. To show the effectiveness of the proposed method, it has been compared with conventional CNN on the isolated words of Aurora2 dataset. The proposed method achieves the average accuracy of 85.96 in noisy train data. It is more robust against Car, Airport and Subway noises with accuracies 90, 88 and 81 in test sets A, B and C, respectively. Results show that the proposed method outperforms conventional CNN with the improvement of 6, 5 and 2 percentage in test set A, test set B and test sets C, respectively. It means that the proposed method is more robust against noisy data and handle these data effectively.Comment: International conference on Pattern Recognition and Image Analysis (IPRIA 2019

About Nonstandard Neutrosophic Logic (Answers to Imamura 'Note on the Definition of Neutrosophic Logic')

In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical real unit interval [0, 1], and a brief evolution of neutrosophic operators. The paper intends to answer Imamura criticism that we found benefic in better understanding the nonstandard neutrosophic logic, although the nonstandard neutrosophic logic was never used in practical applications.Comment: 16 page