Abstract
The application of neuro-fuzzy systems to domains involving prediction and classification of symbolic data requires a reconsideration and a careful definition of the concept of distance between patterns. Traditional distances are inadequate to provide information about the proximity between the symbolic patterns. This work proposes a new architecture of neurofuzzy systems, the Symbolic Adaptive Neuro Fuzzy Inference System (SANFIS) that utilizes effectively a statistically extracted distance measure. The learning approach is a hybrid one and consists of a sequence of steps some of which are essential and some are used in order to optimize further the performance. Initially, a Statistical Distance Metric space is computed from the information provided with the training set. The premise parameters are subsequently evaluated with a three-phase Instance Based Learning (IBL) scheme that estimates the input membership function centers and spreads and constructs the corresponding fuzzy rules. The first phase of this scheme explores heuristic approaches that can uncover information for the relative importance and the reliability of the examples. The second phase exploits this information and extracts an adequate subset of the training patterns for the construction of the fuzzy rules. The concept of fuzzy adaptive subsethood is used at the third phase, for the reduction of the number of the fuzzy sets used as input membership functions. The consequent parameters are estimated with an efficient linear least squares formulation. The obtained performances from the SANFIS trained with the hybrid learning methods are significantly better than the traditional nearest neighbour Instance Based Learning schemes and compares well with advanced neural designs. At the same time SANFIS provides an enhanced explanation ability with the construction of a few interpretable rules.