Paper:

# Fuzzy Rule Interpolation and Extrapolation Techniques: Criteria and Evaluation Guidelines

## Domonkos Tikk^{*1}, Zsolt Csaba Johanyák^{*2},

Szilveszter Kovács^{*3}, and Kok Wai Wong^{*4}

^{*1}Dep. of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Magyar tudósok krt. 2, H-1117 Budapest, Hungary

^{*2}Institute of Information Technology, Kecskemét College, Izsáki út 10, H-6000 Kecskemét, Hungary

^{*3}Department of Information Technology, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary

^{*4}School of Information Technology, Murdoch University, South St., Murdoch, Western Australia 6150, Australia

This paper comprehensively analyzes Fuzzy Rule Interpolation and extrapolation Techniques (FRITs). Because extrapolation techniques are usually extensions of fuzzy rule interpolation, we treat them both as approximation techniques designed to be applied where sparse or incomplete fuzzy rule bases are used, i.e., when classical inference fails. FRITs have been investigated in the literature from aspects such as applicability to control problems, usefulness regarding complexity reduction and logic. Our objectives are to create an overall FRIT standard with a general set of criteria and to set a framework for guiding their classification and comparison. This paper is our initial investigation of FRITs. We plan to analyze details in later papers on how individual techniques satisfy the groups of criteria we propose. For analysis,MATLAB FRI Toolbox provides an easy-to-use testbed, as shown in experiments.

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