Evaluation of Fuzzy Measures Using Dempster–Shafer Belief Structure: A Classifier Fusion Framework

Abstract

This paper studies the high complexity of the calculation of fuzzy measures which can be used in fuzzy integrals to combine the decisions of different learning algorithms. To this end, this paper proposes an alternative low complexity method for the calculation of fuzzy measures that have been applied to Choquet integral for the fusion of deep learning models across different application domains for increasing the accuracy of the overall model. The paper shows that the Dempster-Shafer (DS) belief structure provides partial information about the fuzzy measures associated with a variable, and the paper devises a method to use this partial information for the calculation of fuzzy measures. An infinite number of fuzzy measures is associated with the DS belief structure. This paper proposes a theorem to calculate the general form of a specific set of fuzzy measures associated with the DS belief structure. This specific set of fuzzy measures can be expressed as a weighted summation of the basic assignment function of the DS belief structure. The main advantage of expressing the fuzzy measures in this format is that the monotonic condition which needs to be maintained during the calculation of the fuzzy measure can be avoided and only the basic assignment function needs to be evaluated. The calculation of the basic assignment function is formulated using a method inspired by the Monte Carlo approach used to calculate Value Functions in Markov Decision Process.