On redundancies in systems of fuzzy/linguistic IF–THEN rules under perception-based logical deduction inference

In this study, we formally investigate how to determine fuzzy/linguistic IF–THEN rules that are redundant in linguistic descriptions (systems of IF–THEN rules). We present a formal definition of redundancy and show that seemingly redundant rules can in fact be indispensable. These results apply to IF–THEN rules that use evaluative expressions (e.g., small and very big) and the inference method called perception-based logical deduction. However, they are also valid for inference systems with compatible design choices. We also describe an algorithm for the automatic detection and removal of redundant rules. Finally, we present an example of a linguistic description that is learned automatically from data and reduced using our algorithm.