Theory and Design of a Hybrid Pattern Recognition System

Pattern recognition methods can be divided into four di erent categories: statistical or probabilistic, structural, possibilistic or fuzzy, and neural methods. A formal analysis shows that there is a computational complexity versus representational power trade-o between probabilistic and possibilistic or fuzzy set measures, in general. Furthermore, sigmoidal theory shows that fuzzy set membership can be represented e ectively by sigmoidal functions. Those results and the formalization of sigmoidal functions and subsequently multi-sigmoidal functions and neural networks led to the development of a hybrid pattern recognition system called tFPR. tFPR is a hybrid fuzzy, neural, and structural pattern recognition system that uses fuzzy sets to represent multi-variate pattern classes that can be either static or dynamic depending on time or some other parameter space. Given a set of input data and a pattern class speci cation, tFPR estimates the degree of membership of the data in the fuzzy set that corresponds to the current pattern class. The input data may be a number of timedependent signals whose past values may in uence the evaluation of the pattern class. The membership functions of the fuzzy sets that represent pattern classes are modeled in three di erent ways. In case of relatively simple pattern classes or pattern classes that can be described concisely by a fuzzy set expression, the membership functions of the corresponding fuzzy sets would be modeled by a collection of sigmoidal functions. The choice of sigmoidal functions was motivated by their ability to represent e ciently and concisely di erent multi-variate pattern classes via fuzzy set membership. However, when the pattern class under question would depend on some parameter space (such as time) a structural pattern recognition method (that may involve fuzzy components) would be employed in order to match curves (rather than points) in the input domain. Finally, whenever it would be di cult to obtain a formal de nition of the membership function of a fuzzy set representation for a pattern class, tFPR would model the membership function