Neutrosophic Graph Image Representation Shimaa Fathi Ali1, Hewayda ElGhawalby2 and A.A. Salama3 1,2Egypt, Port Said University, Faculty of Engineering, Physics and Engineering Mathematics Department Shaimaa_ f_a@eng.psu.edu.eg, hewayda2011@eng.psu.edu.eg 3Egypt,Port Said University, Faculty of Science, Department of Mathematics and Computer Science drsalama44@gmail.com

Abstract We transform the intensity (grey scale)image as mathematical object (Spatial Domain) where an image mathematically represented by an m n matrix , with entities g (i, j) corresponding to the intensity to the given pixel located at the node (i, j) to the neutrosophic graph , with its components are very useful in medical diagnoses and medical rays from its medical images and possible applications to nursing research data.  

Many fields such as medical computer vision, medical scene analysis, chemistry and molecular biology have applications in which images have to be processed and some regions have to be searched for and identified. When this processing is to be performed by a computer automatically a useful way of representing the knowledge is by using graphs. Graphs have been proved as an effective way of representing objects by Eshera and Fu, 1986.

When using graphs to represent objects or images, vertices usually represent regions or features of the object or images, and edges between them represent the relations between regions. Clustering plays an important role in data mining, pattern recognition, and machine learning. Clustering data sets into disjoint groups is a problem arising in many domains. Generally, the goal of clustering is to find groups that are both homogeneous and well separated, that is, entities within the same group should be similar and entities in different groups dissimilar.

 

 

 

 

 

Neutrosophic Graph  

 

 

Neutrosophic Graph Clustering Neutrosophic Cluster analysis tries to divide a set of neutrosophic data points into useful or meaningful groups, and it's going to be used in a wide variety of fields: psychology and other social sciences, biology, statistics, pattern recognition, information retrieval, machine learning, and data mining. Neutrosophic Cluster analysis is a challenging task and there are a number of well-known issues associated with it, e.g., finding clusters in neutrosophic data where there are clusters of different shapes, sizes, and density or where the neutrosophic data has lots of noise and outliers. These issues become more important in the context of high dimensionality data sets.

Neutrosophic Graph Image Similarity We introduced neutrosophic graph similarity measures, based on the concept of Haussdorff distance and some of its variants. Firstly, we propose two new neutrosophic dissimilarity measures based on the classical and the modified Haussdorff distances. Basically the neutrosophic dissimilarity measure is a triple: the first part is a dissimilarity measure of the true value of the neutrosophic object, the second part is a dissimilarity measure of the indeterminate value of the neutrosophic object, and the third part is a dissimilarity measure of the false value of the neutrosophic object;

that is the opposite of the neutrosophic object that is the opposite of the neutrosophic object. Secondly, we propose a new neutrosophic similarity measure based on the probabilistic Haussdorff distance . With a similar structure, the neutrosophic similarity measure is also a triple as the explained in the neutrosophic dissimilarity measure. Obviously, if the indeterminate part does not exist (its measure is zero) and if the measure of the opposite object is ignored the suggested neutrosophic dissimilarity measure is reduced to the concept of Haussdorff distance in the fuzzy sense.

Neutrosophic Clustering Low Dimensional Data