Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm

Journal of Intelligent Systems

Kandasamy Ilanthenral¹ 

[1] School of Computer Science and Engineering, VIT University, Vellore, India;

关键词: neutrosophic set;    double-valued neutrosophic set (dvns);    minimum spanning tree (mst);    clustering algorithm;    double-valued neutrosophic minimum spanning tree (dvn-mst) clustering algorithm;    62h30;    05c90;    03b52;    03b60;   

DOI  :  10.1515/jisys-2016-0088

来源: DOAJ

【 摘 要 】

Neutrosophy (neutrosophic logic) is used to represent uncertain, indeterminate, and inconsistent information available in the real world. This article proposes a method to provide more sensitivity and precision to indeterminacy, by classifying the indeterminate concept/value into two based on membership: one as indeterminacy leaning towards truth membership and the other as indeterminacy leaning towards false membership. This paper introduces a modified form of a neutrosophic set, called Double-Valued Neutrosophic Set (DVNS), which has these two distinct indeterminate values. Its related properties and axioms are defined and illustrated in this paper. An important role is played by clustering in several fields of research in the form of data mining, pattern recognition, and machine learning. DVNS is better equipped at dealing with indeterminate and inconsistent information, with more accuracy, than the Single-Valued Neutrosophic Set, which fuzzy sets and intuitionistic fuzzy sets are incapable of. A generalised distance measure between DVNSs and the related distance matrix is defined, based on which a clustering algorithm is constructed. This article proposes a Double-Valued Neutrosophic Minimum Spanning Tree (DVN-MST) clustering algorithm, to cluster the data represented by double-valued neutrosophic information. Illustrative examples are given to demonstrate the applications and effectiveness of this clustering algorithm. A comparative study of the DVN-MST clustering algorithm with other clustering algorithms like Single-Valued Neutrosophic Minimum Spanning Tree, Intuitionistic Fuzzy Minimum Spanning Tree, and Fuzzy Minimum Spanning Tree is carried out.

【 授权许可】

Unknown