Type-Reduction of the Discretised Interval Type-2 Fuzzy Set: Approaching the Continuous Case through Progressively Finer Discretisation

The defuzzification of a type-2 fuzzy set is a two stage process consisting of firstly type-reduction, and secondly defuzzification of the resultant type-1 set. This paper considers three approaches to discrete interval type-reduction: 1. The exhaustive method which produces the TypeReduced Set, 2. the Greenfield-Chiclana Collapsing Defuzzifier which gives rise to the Representative Embedded Set Approximation, and 3. the Nie-Tan Method from which the Nie-Tan Set is derived. In the discrete case these three type-1 sets are distinct. The behaviour of the three sets under fine discretisation is investigated experimentally, in order to shed light on the relationships between the continuous versions of these type-1 sets.