Agglomerative Hierarchical Clustering Method under Neutrosophic Trapezoidal Fuzzy Numbers

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.