ABSTRACT
This chapter deals with the problem of linear discriminant functions for fuzzy classes. For the case of two classes, a fuzzy version of Fisher discriminant function is given. Multiple fuzzy discriminant analysis is also considered. Some clustering criteria based on fuzzy scatter matrices are given. The approach of fuzzy discriminant analysis considered in this chapter is mainly based on the papers [4], [5], and parallels the classical one (see, for instance, [3] or [10]). Gradient methods or other structural optimization methods are not appropriate tools to deal with the criterion functions obtained by using fuzzy discriminant analysis. To solve optimization problems based on scattering criteria, we may successfully use a genetic algorithm-based approach. A combination of simulated annealing [14] and tabu search [9] could also be appropriate.
