Interval Type-2 Mutual Subsethood Fuzzy Neural Inference System (IT2MSFuNIS)

Abstract

This paper presents an interval type-2 mutual subsethood fuzzy neural inference system (IT2MSFuNIS). A mutual subsethood measure between two interval type-2 fuzzy sets (IT2 FS) has been derived and has been used in determining the similarity between the IT2 FS inputs and IT2 FS antecedents. The consequent weights are taken to be interval sets. The inputs to the system are fuzzified into IT2 FSs with Gaussian primary membership function having fixed center and uncertain variance. Aggregation of type-2 mutual subsethood based activation spreads is performed using product operator. The output is obtained using simplified type-reduction followed by defuzzification. The system learns using memetic procedure involving differential evolution for global search and gradient descent for local exploitation in solution space. The mathematical modeling and empirical studies of IT2MSFuNIS bring forth its efficacy in problems pertaining to function approximation, time-series prediction, control, and classification. Comparisons with other type-1 and type-2 neuro-fuzzy systems verify that IT2MSFuNIS compares excellently with other models with a performance better than most of them both in terms of total number of trainable parameters and result accuracy. Empirical studies indicate the intelligent decision making capability of the proposed model. The main contribution of this paper lies in the identification of mutual subsethood to find out the correlation between IT2 FSs and to find out its applicability in diverse application domains. The improved performance of the proposed method can be attributed to the better contrast handling capacity of mutual subsethood method and uncertainty handling capacity of IT2 FSs. The integration of mutual subsethood with interval type-2 fuzzy logic puts forth a novel model with various merits as demonstrated amply with the help of well-known problems reported in the literature.