A procedure for the generation of interval type-2 membership functions from data

Display OmittedSketch of the proposed procedure including the DE & DE-TA hybrid metaheuristics. Proposes a new interval type-2 membership function called extended interval type-2 membership function.Presents a new procedure for generating a set of extended interval type-2 membership functions for an interval type-2 linguistic variable from data.Shows the working of the proposed procedure with real world data.Discusses the effects of distance measures and initial solutions. This paper proposes a new interval type-2 fuzzy set taking extended interval type-2 membership function (IT2 MF) as its values, and presents a new procedure for generating a set of extended IT2 MFs from data for an interval type-2 linguistic variable. An extended IT2 MF is defined as the min and max of two extended (type-1 or ordinary) membership functions. The procedure has the following steps: (i) for each interval type-2 linguistic variable, specifying the number of membership functions to be generated, i.e. the granularity level, (ii) choosing two fuzzy exponents to be used, (iii) for each fuzzy exponent, applying the fuzzy c-means variant (FCMV) proposed by Liao et al. [1] to obtain the corresponding centers and membership values, and (iv) carrying out parametric optimization by applying a metaheuristic or a hybrid metaheuristic algorithm to determine the optimal parameters associated with the extended IT2 MFs so that the mean squared error (MSE) or sum of squared errors (SSE) between the membership values obtained by FCMV and those predicted by the extended IT2 MFs is minimized. The proposed procedure was illustrated with an example and further tested with iris data and weld data. The effects of using two different interval distance measures and the cluster means obtained by the FCMV as part of the initial solutions in the differential evolution metaheuristic were also investigated and discussed.