TY - JOUR

T1 - Minimum spanning tree hierarchical clustering algorithm

T2 - A new Pythagorean fuzzy similarity measure for the analysis of functional brain networks

AU - Habib, Amna

AU - Akram, Muhammad

AU - Kahraman, Cengiz

N1 - Publisher Copyright:
© 2022

PY - 2022/9/1

Y1 - 2022/9/1

N2 - Clustering structures are one of the most important aspects of complex networks. Minimum spanning tree (MST), the tree that connects all vertices with minimum total weight, can be considered as a fundamental unit of original weighted graphs. There are different types of algorithms that identify clusters in a network, but the existing theories and algorithms for searching trees have not been investigated for uncertain scenarios. This paper tackles the situations where network parameters may be uncertain. Rather, we permit the parameters to take the form of Pythagorean fuzzy numbers (PFNs). Moreover, to represent qualitative aspects of uncertainty, the use of linguistic variables (LVs) has effective means for experts in expressing their views. The current study proposes a graph theory-based agglomerative hierarchical clustering technique for Pythagorean fuzzy sets. We first define generalized Pythagorean fuzzy numbers (GPFNs) and LR-type PFNs. Then we compute the PF distance between two GPFNs and also LR-type PFNs, and formulate the expressions for PF similarity measure. This paper mainly examines the use of PF distance and similarity measures in a minimum spanning tree agglomerative hierarchical clustering method by considering PFLVs. Since the structural and functional systems of brain are characterized by complex networks, we apply the proposed algorithm on a functional brain network to prove its practicality and efficiency. We discuss the hierarchical clustering consequences of the proposed algorithm in the shape of a dendrogram. Finally, we compare the clustering results obtained by different similarity measures.

AB - Clustering structures are one of the most important aspects of complex networks. Minimum spanning tree (MST), the tree that connects all vertices with minimum total weight, can be considered as a fundamental unit of original weighted graphs. There are different types of algorithms that identify clusters in a network, but the existing theories and algorithms for searching trees have not been investigated for uncertain scenarios. This paper tackles the situations where network parameters may be uncertain. Rather, we permit the parameters to take the form of Pythagorean fuzzy numbers (PFNs). Moreover, to represent qualitative aspects of uncertainty, the use of linguistic variables (LVs) has effective means for experts in expressing their views. The current study proposes a graph theory-based agglomerative hierarchical clustering technique for Pythagorean fuzzy sets. We first define generalized Pythagorean fuzzy numbers (GPFNs) and LR-type PFNs. Then we compute the PF distance between two GPFNs and also LR-type PFNs, and formulate the expressions for PF similarity measure. This paper mainly examines the use of PF distance and similarity measures in a minimum spanning tree agglomerative hierarchical clustering method by considering PFLVs. Since the structural and functional systems of brain are characterized by complex networks, we apply the proposed algorithm on a functional brain network to prove its practicality and efficiency. We discuss the hierarchical clustering consequences of the proposed algorithm in the shape of a dendrogram. Finally, we compare the clustering results obtained by different similarity measures.

KW - Distance measure

KW - Generalized Pythagorean fuzzy number

KW - Hierarchical clustering

KW - Minimum spanning tree

KW - Similarity measure

UR - http://www.scopus.com/inward/record.url?scp=85128535689&partnerID=8YFLogxK

U2 - 10.1016/j.eswa.2022.117016

DO - 10.1016/j.eswa.2022.117016

M3 - Article

AN - SCOPUS:85128535689

SN - 0957-4174

VL - 201

JO - Expert Systems with Applications

JF - Expert Systems with Applications

M1 - 117016

ER -