Type-reduction of the discretised interval type-2 fuzzy set

Authors:
Sarah Greenfield;Francisco Chiclana;Robert John
Affiliations:
Centre for Computational Intelligence, De Montfort University, Leicester, UK;Centre for Computational Intelligence, De Montfort University, Leicester, UK;Centre for Computational Intelligence, De Montfort University, Leicester, UK
Venue:
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Year:
2009

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Abstract

We begin by surveying the available strategies for type-reducing a discretised type-2 fuzzy set to a type-1 fuzzy set, namely the exhaustive method, the Karnik-Mendel Iterative Procedure, the sampling method, the Greenfield-Chiclana Collapsing Defuzzifier and the Nie-Tan method. We go on to investigate mathematically what happens to the Representative Embedded Set Approximation as the domain discretisation becomes finer. This leads into a discussion of the relationship between the collapsing and Nie-Tan methods. An experimental comparison is made between the collapsing and Nie-Tan methods, with respect to both efficiency and accuracy.