Hierarchical Granular Clustering: An Emergence of Information Granules of Higher Type and Higher Order

Witold Pedrycz*, Rami Al-Hmouz, Abdullah Saeed Balamash, Ali Morfeq

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)

Abstract

In this study, we introduce a concept of hierarchical granular clustering and establish its algorithmic framework. We show that the proposed model naturally gives rise to information granules that are both of higher order and higher type, offering a compelling justification behind their emergence. In a concise way, we can capture the overall architecture of information granules as a hierarchy exhibiting conceptual layers of increasing abstraction: numeric data → information granules → information granules of type-2, order-2 →... information granules of higher type/order. The elevated type of information granules is reflective of the visible hierarchical facet of processing and the inherent diversity of the individual locally revealed structures in data. While the concept and the methodology deliver some general settings, the detailed algorithmic aspects are discussed in detail when using fuzzy clustering realized by means of fuzzy c-means. Furthermore, for illustrative purposes, we mainly focus on interval-valued fuzzy sets and granular interval fuzzy sets arising at the higher level of the hierarchy. Higher type fuzzy sets are formed with the help of the principle of justifiable granularity. The conceptually sound hierarchy is established in a general way, which makes it equally applicable to various formalisms of representation of information granules. Experiments are reported for synthetic and publicly available datasets.

Original languageEnglish
Article number7073607
Pages (from-to)2270-2283
Number of pages14
JournalIEEE Transactions on Fuzzy Systems
Volume23
Issue number6
DOIs
Publication statusPublished - Dec 1 2015
Externally publishedYes

Keywords

  • granular
  • hierarchical collaborative clustering
  • information granules of higher type and higher order

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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