Fuzzy Min-Max Neural Networks-Part 1 : Classification
Patrick K. Simpson · 1992
A supervised learning neural network classifier that utilizes fuzzy sets as pattern classes is described. Each fuzzy set is an aggregate (union) of fuzzy set hyperboxes. A fuzzy set hyperbox is an n-dimensional box defined by a min point and a max point with a corresponding membership function. The min-max points are determined using the fuzzy min-max learning algorithm, an expansionxontraction process that can learn nonlinear class boundaries in a single pass through the data and provides the ability to incorporate new and refine existing classes without retraining. The use of a fuzzy set approach to pattern classification inherently provides degree of membership information that is extremely useful in higher level decision mak- ing. This paper will describe the relationship between fuzzy sets and pattern classification. It explains the fuzzy min-max classifier neural network implementation, it outlines the learning and recall algorithms, and it provides several examples of operation that demonstrate the strong qualities of this new neural network classifier. AmRN classification is a key element to many engi- P neering solutions. Sonar, radar, seismic, and diagnostic applications all require the ability to accurately classify a situation. Control, tracking, and prediction systems will often use classifiers to determine input-output relationships. Because of this wide range of applicability, pattern classification has been studied a great deal (13), (15), (19). This paper describes a neural network classifier that creates classes by aggregating several smaller fuzzy sets into a single fuzzy set class. This technique, introduced in (42) as an extension of earlier work (41), can learn pattern classes in a single pass through the data, it can add new pattern classes on the fly, it can refine existing pattern classes as new information is received, and it uses simple operations that allow for quick execution. Fuzzy min-max classification neural networks are built using hyperbox fuzzy sets. A hyperbox defines a region of the n-dimensional pattern space that has patterns with full class membership. A hyperbox is completely defined by its min point and its max point, and a membership function is defined with respect to these hyperbox min-max points. The min-max (hyperbox) membership function combination defines a fuzzy set, hyperbox fuzzy sets are aggregated to form a single fuzzy set class, and the resulting structure fits naturally into a neural network framework; hence this classification system is called a fuzzy min-max classification neural network. Learning in the fuzzy min-max classification neural network is performed by properly placing and adjusting hyperboxes in the pattern space.