Defuzzification of the Discretised Generalised Type-2 Fuzzy Set: Experimental Evaluation

Date

2013

Advisors

Journal Title

Journal ISSN

ISSN

Volume Title

Publisher

Elsevier

Type

Article

Peer reviewed

Yes

Abstract

The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type-2 fuzzy sets as created by the inference stage of a Mamdani Fuzzy Inferencing System. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this defuzzification bottleneck. In this paper we begin by surveying the main alternative strategies for defuzzifying a generalised type-2 fuzzy set: (1) Vertical Slice Centroid Type-Reduction; (2) the sampling method; (3) the elite sampling method; and (4) the α-planes method.

We then evaluate the different methods experimentally for accuracy and efficiency. For accuracy the exhaustive method is used as the standard. The test results are analysed statistically by means of the Wilcoxon Nonparametric Test and the elite sampling method shown to be the most accurate. In regards to efficiency, Vertical Slice Centroid Type-Reduction is demonstrated to be the fastest technique.

Description

CCI - Centre for Computational Intelligence NOTICE: this is the author’s version of a work that was accepted for publication in Information Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version can be found by following the DOI

Keywords

Type-2 fuzzy sets, Defuzzification, Sampling Method, $\alpha$-Planes Method, VSCTR

Citation

Greenfield, S. and Chiclana, F. (2013) Defuzzification of the Discretised Generalised Type-2 Fuzzy Set: Experimental Evaluation. Information Sciences, 244, pp. 1-25

Rights

Research Institute

Institute of Artificial Intelligence (IAI)