Agglomerative Hierarchical Clustering Method under  Neutrosophic Trapezoidal Fuzzy Numbers

Madineh Farnam; Gholam Hassan Shirde; Majid Darehmirak

Authors

Madineh Farnam Department of Electrical Engineering, Shohadaye Hoveizeh Campus of Technology, Shahid Chamran University of Ahvaz, Dasht-e Azadegan, Khuzestan, Iran;
Gholam Hassan Shirde Department of Mathematic, Faculty of Basic Sciences, University of Qom, Qom, Iran;
Majid Darehmirak Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khouzestan, Iran;

Keywords:

clustering; agglomerative hierarchical clustering; neutrosophic set; neutrosophic trapezoidal fuzzy number; distance measure

Abstract

Clustering, as one of the most basic data mining strategies, has a prominent role in various
fields of application, especially decision making in management systems. Experts can make and
implement decisions according to the features of each cluster by examining the characteristics,
nature, and essence of the data that are in the same cluster. Since neutrosophic sets in various
application fields have inspired tremendous research endeavors to model problems from varius of
aspects, the main goal of this research is to combine hierarchical clustering with neutrosophic
trapezoidal fuzzy data. For this purpose, a new distance measure is first introduced to calculate the
difference between neutrosophic trapezoidal fuzzy data. In the following, while proving some
characteristics of the measure, the hierarchical clustering algorithm based on the new distance
measure with neutrosophic trapezoidal fuzzy data is explained. By extending continuous fuzzy data
from an explanatory example in fuzzy literature, the effectiveness and efficiency of the proposed
algorithm are tested in MATLAB software. Although the resulting dendrogram provides
appropriate clustering to the decision maker, two criteria gap, and silhouette, are also used to
determine the optimal number of clusters. The hybrid process developed in this research can not
only be used in the study areas of clustering but also makes it possible to propose the optimal
number of clusters for neutrosophic trapezoidal fuzzy data.