@inproceedings{52c92273d1ec4babb3fec4fae4fcddbb,
title = "Fuzzy Equivalence Relations as Similarity Measure in Agglomerative Clustering Algorithm",
abstract = "This chapter studies hierarchical clustering, particularly agglomerative clustering, where fuzzy equivalence relations are considered as a measure of the similarity of objects and clusters, in which transitivity is defined on the basis of various t-norms: {\L}ukasiewicz, product, and Hamacher{\textquoteright}s t-norm. In construction of fuzzy equivalence relation is involved a tool called an additive generator. For objects and clusters, internal and external similarities are introduced using aggregation of corresponding equivalence relations. In the paper, a quality measure of the cluster system is presented using fuzzy equivalence relations. Additionally, the paper provides a comparative analysis between standard clustering methods (KMeans, C-Means) and the proposed method, with fuzzy equivalence relations, where transitivity is defined on the basis of t-norms.",
keywords = "Additive generator, Agglomerative clustering algorithm, Aggregation of fuzzy equivalence relations, Similarity measure, t-norms",
author = "Valērijs Mihailovs",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.",
year = "2025",
doi = "10.1007/978-981-97-9324-2\_39",
language = "English",
isbn = "978-981979323-5",
series = "Lecture Notes in Networks and Systems",
pages = "497--508",
editor = "Atulya Nagar and Jat, \{Dharm Singh\} and Durgesh Mishra and Amit Joshi",
booktitle = "Intelligent Sustainable Systems - Selected Papers of WorldS4 2024",
}