In recent years, successful applications of singleton fuzzy inference systems have been made in a plethora of different kinds of problems, for example in the areas of control, digital image processing, time series prediction, fault detection and classification. However, there exists another relatively less explored approach, which is the use of non-singleton fuzzy inference systems. This approach offers an interesting way for handling uncertainty in complex problems by considering inputs with uncertainty, while the conventional Fuzzy Systems have their inputs with crisp values (singleton systems). Non-singleton systems have as inputs Type-1 membership functions, and this difference increases the complexity of the fuzzification, but provides the systems with additional non-linearities and robustness. The main limitations of using a non-singleton fuzzy inference system is that it requires an additional computational overhead and are usually more difficult to apply in some problems. Based on these limitations, we propose in this work an approach for efficiently processing non-singleton fuzzy systems. To verify the advantages of the proposed approach we consider the case of general type-2 fuzzy systems with non-singleton inputs and their application in the classification area. The main contribution of the paper is the implementation of non-singleton General Type-2 Fuzzy Inference Systems for the classification task, aiming at analyzing its potential advantage in classification problems. In the present paper we propose that the use of non-singleton inputs in Type-2 Fuzzy Classifiers can improve the classification rate and based on the realized experiments we can observe that General Type-2 Fuzzy Classifiers, but with non-singleton fuzzification, obtain better results in comparison with respect to their singleton counterparts.
Determination of the number of clusters used in fuzzy inference systems by means of K-means and modeling of dam volume: Kestel dam example
