The Sampling Method of Defuzzification for Type-2 Fuzzy Sets: Experimental Evaluation Sarah Greenfield a , Francisco Chiclana a , Robert John a , Simon Coupland a a Centre for Computational Intelligence, Faculty of Technology De Montfort University, Leicester LE1 9BH, UK {sarahg, chiclana, rij, simonc}@dmu.ac.uk Abstract For generalised type-2 fuzzy sets the defuzzification process has historically been slow and inefficient. This has hampered the development of type-2 Fuzzy Inferencing Systems for real applications and therefore no advantage has been taken of the ability of type-2 fuzzy sets to model higher levels of uncertainty. The research reported here provides a novel approach for improving the speed of defuzzification for discretised generalised type-2 fuzzy sets. The traditional type-reduction method requires every embedded type-2 fuzzy set to be processed. The high level of redundancy in the huge number of embedded sets inspired the development of our sampling method which randomly samples the embedded sets and processes only the sample. The paper presents detailed experimental results for defuzzification of constructed sets of known defuzzified value. The sampling defuzzifier is compared on aggregated type-2 fuzzy sets resulting from the inferencing stage of a FIS, in terms of accuracy and speed, with other methods including the exhaustive and techniques based on the α-planes representation. The results indicate that by taking only a sample of the embedded sets we are able to dramatically reduce the time taken to process a type-2 fuzzy set with very little loss in accuracy. Keywords: Type-2 Fuzzy Set, Defuzzification, Sampling Method, Type-Reduced Set, Type-Reduction 1. Introduction The main strength of type-2 fuzzy logic is its ability to deal with the second-order un- certainties that arise from several sources [14], among them the fact that the meanings of words are often vague [23, page 117]. Most researchers concentrate exclusively on interval secondary membership functions [22, 23] for which an increasing number of applications are being developed [1, 5, 10, 11, 15–18, 20, 25, 26, 35]. The Karnik-Mendel Iterative Procedure (KMIP) [13, 30] is the established technique for defuzzification of interval sets. The capability of the generalised type-2 paradigm to handle uncertainty is explored in [9]. Regrettably interval type-2 fuzzy sets are not able to model uncertainty as fully as their generalised counterparts, as they lack the crucial variability of the third dimension [23]. Our research, therefore, sees developing generalised type-2 systems as a challenge for the research community. A triangular type-2 system with a defuzzification algorithm based on the KMIP has been developed by Starczewski [28]; this goes some way towards achieving our goal. Coupland and John [2, 3] have exploited geometry to improve the speed of inferencing in generalised type-2 fuzzy sets. In 2008 Liu [19, 24] proposed the Preprint submitted to Information Sciences November 3, 2011