A consistent algorithm based on similarity measure with thresholds

The property of being consistent is most important for any fuzzy reasoning method. In this paper, the definitions of the consistencies of Generalized Modus Ponens (GMP) and Generalized Modus Tollens (GMT) for multiple rules with thresholds are proposed. Then some examples are given to show the existing fuzzy reasoning methods are not generally consistent for multiple rules. Consequently, a consistent algorithm based on similarity measure with thresholds is proposed, which is proved to be consistent for multiple rules. Finally, some results are given to show that the consistent algorithm based on similarity measure with thresholds is workable.