A study of type-2 fuzzy clustering

Fuzzy C-means (FCM) has been a prominent clustering algorithm for a long time. It was extended to a type-2 framework by the linguistic fuzzy C-means (LFCM) algorithm that operates on vectors of fuzzy numbers utilizing the extension principle, the decomposition theorem, and interval analyses. The purpose of this thesis is to investigate the iterative type-2 fuzzy clustering algorithms. The LFCM incorporates uncertainty through type-2 fuzzy sets, but it is prone to membership spread, i.e., the uncertainty in a membership function can become too large or broad during the iterative alternating optimization procedure. We devise three dampening approaches to mitigate this problem. Vertical cut dampening, linear dampening, and reflection dampening are defined along with the experiments conducted on a synthetic dataset named the butterfly dataset. We also illustrate the updated memberships (fuzzy numbers) and the resulting cluster prototypes (fuzzy vectors) from visual standpoints. Applying any of these dampening approaches will result in thinner membership functions and helps us control the uncertainty, and in fact, aid in convergence. The linguistic possibilistic C-means (LPCM), which is a type-2 version of the possibilistic C-means (PCM) algorithm, is also studied, and compared to LFCM. We also address some practical guidelines for putting the type-2 fuzzy clustering algorithms into action.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Computer science (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2022

Author dc:creator

• Chantapakul, Watchanan

Advisor dc:contributor.advisor

• Keller, James M.

Language dc:language.iso

eng, English

DOI

https://doi.org/10.32469/10355/91493

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/91493