Fuzzy learning model for membership function estimation and pattern classification

In this paper, a new fuzzy learning model called fuzzy learning vector quantization (FLVQ) which incorporates fuzzy clustering concept with Kohonen's learning vector quantization (LVQ) model is proposed. The new learning algorithm is derived from optimizing an appropriate fuzzy objective function which takes into accounts of two goals, namely, minimizing the differences between target and actual class membership outputs, and minimizing the distances between training patterns and neuron's parametric vectors. It retains the LVQ's reinforce-or-punish learning principle and more importantly introduces graded corrections. As compared with the LVQ algorithm, the proposed one is characterized by several distinctive features: i) avoiding neuron underutilization; ii) superior classification and generalization performances; and iii) insensitive to initial conditions. Since the outputs of the model have been formulated as fuzzy class membership functions, it can be readily used to estimate the membership functions of fuzzy systems. Furthermore, through the concept of 'clusters as rules', the trained network can be interpreted in the form of fuzzy IF-THEN rules. All these features of the proposed model are demonstrated through numerical examples.