Vector-valued Choquet Integral Models

Abstract

Some types of Vector-valued Choquet integral models are proposed. For an input vector x = (x_1,..., x_n)^T, the output y = (y_1,..., y_m)^T is calculated by the m times (extended) Choquet integral with respect to the jth fuzzy measure mu_j. The vector-valued Choquet integral model is an extension of the product calculation between a matrix and a vector. The logical type vector-valued Choquet integral models enable to do classifications. If the sum of fuzzy measure values among fuzzy measures equal to 1 for all sets, the sum of output values is 1. Lastly, we propose a classification method with overlapping and unclassified degrees from ordinal classification by fuzzy rules.