Fuzzy rule-base modeling is the task of identifying the structure and the parameters of a fuzzy if-then rule base so that a desired input/output mapping is achieved. Recently, using adaptive networks to fine-tune membership functions in a fuzzy rule base has received more and more attention. In this paper we summarize Jang’s architecture of employing an adaptive network and the Kalman filtering algorithm to identify the system parameters. Given a surface structure, the adaptively adjusted inference system performs well on a number of interpolation problems. We generalize Jang’s basic model so that it can be used to solve classification problems by employing parameterized t-norms. We also enhance the model to include weights of importance so that feature selection becomes a component of the modeling scheme. Next, we discuss two ways of identifying system structures based on Jang’s architecture. For the top-down approach, we summarize several ways of partitioning the feature space and propose a method of using clustering objective functions to evaluate possible partitions. We analyze the overall learning and operation complexity. In particular, we pinpoint the dilemma between two desired properties: modeling accuracy and pattern matching efficiency. Based on the analysis, we suggest a bottom-up approach of using rule organization to meet the conflicting requirements. We introduce a data structure, called a fuzzy binary boxtree, to organize rules so that the rule base can be matched against input signals with logarithmic efficiency. To preserve the advantage of parallel processing assumed in fuzzy rule-based inference systems, we give a parallel algorithm for pattern matching with a linear speedup. Moreover, as we consider the communication and storage cost of an interpolation model, it is important to extract the essential components of the modeled system and use the rest as a backup. We propose a rule combination mechanism to build a simplified version of the original rule base according to a given focus set. This scheme can be used in various situations of pattern representation or data compression, such as in image coding or in hierarchical pattern recognition.