The information content of fuzzy relations and fuzzy rules

Based on different emphases, some general information content measures of fuzzy relations are given. Distinguished from the measures related to fuzzy relations proposed before, these measures try to estimate the information conveyed by multiple-domain fuzzy relations without preassigned probability distribution. Since fuzzy rules can be fully captured by fuzzy relations from an input universe to an output universe, the information content of fuzzy rules can be easily measured by the information content of fuzzy relations proposed by us. However, there also exists a difference between fuzzy relations and fuzzy rules. Rules(especially classification rules) always have a direction from the antecedent and consequent while relations do not have direction. Based on this difference, some general measures for the information content of fuzzy rules are proposed. In practice, these measures can do well in the evaluation and selection of fuzzy rules. Finally, the measures of the information content of fuzzy rules are used to evaluate the stability and sensitivity of fuzzy implication operators in fuzzy control.