Fuzzy Measures and Fuzzy Integrals

One of the advantages of fuzzy set theory is the wide range of computational mechanisms to implement the framework of fusion of multiple sources of information. This chapter helps to develop one of these powerful frameworks, the fuzzy integral. The fuzzy integral is based on the concept of fuzzy measures, generalizations of probability measures, which in themselves will be shown to be effective to combine information in certain applications. The key to using fuzzy integrals to fuse multiple sources of information is to construct fuzzy measures that specify the worth of all subsets of sources of information. For many applications, Sugeno measures are employed. The chapter introduces both the Sugeno and Choquet integrals as generalized expectation operators, and describes a few of the learning algorithms for real problems. It also provides an example to show one successful approach that uses self-organizing feature maps (SOFM) to help generate densities in a word recognition application.