Efficient inference procedures with fuzzy inputs

In fuzzy rule-based systems, allowing for fuzzy inputs and producing accurate fuzzy outputs is necessary in order to process the knowledge in an efficient and correct way. However, if reasoning with fuzzy inputs is easy with Mamdani-like conjunction-based rules, it becomes more difficult with implication-based rules. Indeed, it has been shown that the usual rule-by-rule inference mechanism, Select, Trigger and Combine, should not be used with this kind of rules when facing fuzzy inputs, since it generally leads to unexpectedly too large outputs. Even if implication-based rules present suitable properties, they have not been widely used due to this practical limitation. In this paper, new inference procedures are proposed for certainty rules and gradual rules, and the two main types of implication-based rules are: modeled with Kleene-Dienes and Rescher-Gaines implications, respectively. A solution is given which allows a rule-by-rule inference with certainty rules, and an exact inference algorithm is given for gradual rules which are more difficult to handle.