T S Based Single Valued Neutrosophic Number Equivalence Matrix And Clustering Method

Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms. At present, there exist no results constructing a single-valued neutrosophic number equivalence matrix using t-norm and t-conorm.

Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms.

Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. Neutrosophic set, which is extension of fuzzy set, has received extensive attention in solving many real life problems of uncertainty, inaccuracy, incompleteness, inconsistency and uncertainty.

Clustering algorithm is one of the important research topics in the field of machine learning. Neutrosophic clustering is the generalization of fuzzy clustering and has been applied to many fields. this paper presents a new neutrosophic clustering algorithm with the help of regularization. Firstly, the regularization term is introduced into the FC-PFS algorithm to generate sparsity, which can reduce the complexity of the algorithm on large data sets. Secondly, we propose a method to simplify the process of determining regularization parameters. Finally, experiments show that the clustering results of this algorithm on artificial data sets and real data sets are mostly better than other clustering algorithms. Our clustering algorithm is effective in most cases.

In this study we define the generalizing single valued triangular neutrosophic number. In addition, single valued neutrosophic numbers are transformed into single valued triangular neutrosophic numbers according to the values of truth, indeterminacy and falsity. Furthermore, we extended the Hamming distance given for triangular intuitionistic fuzzy numbers to single valued triangular neutrosophic numbers. We have defined new score functions based on the Hamming distance.

Raw data are classified using clustering techniques in a reasonable manner to create disjoint clusters. A lot of clustering algorithms based on specific parameters have been proposed to access a high volume of datasets. This paper focuses on cluster analysis based on neutrosophic set implication, i.e., a k-means algorithm with a threshold-based clustering technique. This algorithm addresses the shortcomings of the k-means clustering algorithm by overcoming the limitations of the threshold-based clustering algorithm. To evaluate the validity of the proposed method, several validity measures and validity indices are applied to the Iris dataset (from the University of California, Irvine, Machine Learning Repository) along with k-means and threshold-based clustering algorithms. The proposed method results in more segregated datasets with compacted clusters, thus achieving higher validity indices. The method also eliminates the limitations of threshold-based clustering algorithm and validates measures and respective indices along with k-means and threshold-based clustering algorithms.

The fuzzy set and intuitionistic fuzzy set are two useful mathematical tool for dealing with impression and uncertainty. However sometimes these theories may not suffice to model indeterminate and inconsistent information encountered in real world.

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties.