Complexity reduction of rule based models: a survey

Abstract

This paper gives a survey of fuzzy rule base reduction methods. The research of complexity reduction methods are originated form two aspects depending of different design methodologies of the model. The first model design type comes from the original idea of Zadeh, it proposes models which are built based on expert knowledge, hence the rule base is set up manually. These models feature linguistic, and hence semantically interpretable fuzzy terms, and rules with fuzzy sets as consequents. However, it is often the case that the model contains redundant rules and/or variables, so there is a need to omit the redundancy of the model. Secondly, in the last decade data-driven fuzzy model design became more popular. This is partly due to fact that fuzzy models were found to be universal approximators, i.e. they are capable t o approximate with arbitrary accuracy any continuous control function. For fitting the model the possible best to the approximated function, these models, usually having rules with consequents which are linear function of the inputs, use tremendously large number of rules, and do not take into account the complexity and interpretability of the model. This feature also emerged the issue of rule base reduction for such systems. The present paper aims at summarizing the efforts done on the complexity reduction field briefly.

Accuracy-Based Learning Classifier Systems for Multistep Reinforcement Learning: A Fuzzy Logic Approach to Handling Continuous Inputs and Learning Continuous Actions

“…In this case, rule R can be safely removed. Effective reduction of the fuzzy knowledge base has been extensively studied in the literature [37]. Since it is not our main focus, we will not explore this issue any further.…”

Video Shot Boundary Detection Using QR-Decomposition and Gaussian Transition Detection

“…The SVD has been utilized by a great number of researchers for rule base reduction [30,31]. The main reason for using SVD in complexity reduction is that SVD decomposes a given system into different parts and specifies the level of the importance of each decomposed part.…”

A QR decomposition based mixture model algorithm for background modeling

“…R-values are in decreasing order and they tend to track the singular values of P [9]. The singular value decomposition has been used by many people for rule base reduction [9,10]. The key idea of using the singular value decomposition (SVD) in complexity reduction is that the singular values can be applied to decompose a given system and indicate the degree of the significance of the decomposed parts.…”

“…The key idea of using the singular value decomposition (SVD) in complexity reduction is that the singular values can be applied to decompose a given system and indicate the degree of the significance of the decomposed parts. Reduction is conceptually obtained by the truncation of those parts which have weak contribution to the output according to the assigned singular values [10]. We use this feature to distinguish background pixels from foreground ones.…”