Classification of heterogeneous fuzzy data by choquet integral with fuzzy-valued integrand

As a fuzzification of the Choquet integral, the defuzzified choquet integral with fuzzy-valued integrand (DCIFI) takes a fuzzy-valued integrand and gives a crisp-valued integration result. In this paper, the DCIFI acts as a projection to project high-dimensional heterogeneous fuzzy data to one-dimensional crisp data to handle the classification problems involving different data forms, such as crisp data, interval values, fuzzy numbers, and linguistic variables, simultaneously. The nonadditivity of the signed fuzzy measure applied in the DCIFI can represent the interaction among the measurements of features towards the discrimination of classes. Values of the signed fuzzy measure in the DCIFI are considered to be unknown parameters which should be learned before the classifier is used to classify new data. We have implemented a genetic algorithm (GA)-based adaptive classifier-learning algorithm to optimally learn the signed fuzzy measure values and the classified boundaries simultaneously. The performance of our algorithm has been tested both on synthetic and real data. The experimental results are satisfactory and outperform those of existing methods, such as the fuzzy decision trees and the fuzzy-neuro networks.