Non-additive MCLP

Abstract

In order to modeling the interactions among attributes for classification, the non-additive measures are studied in this chapter. The non-additive measures provide very important information regarding the interactions among attributes and potentially useful for data mining. The concept of non-additive measures (also referred to as fuzzy measure theory) was initiated in the 1950s and have been well developed since 1970s. Nonadditive measures have been successfully used as a data aggregation tool for many applications such as information fusion, multiple regressions and classifications. The nonlinear integrals are the aggregation tools for the non-additive measures. The Choquet integral, a nonlinear integral, is utilized to aggregate the feature attributes with respect to the non-additive measure. The non-additive MCLP classification models are constructed in this chapter, and because the using of non-additive measure increases the computational cost, two major solutions to reduce the number of non-additive measures are given: hierarchical Choquet integral and the K-additive measure.