Optimal fuzzy reasoning and its robustness analysis

Fuzzy reasoning methods are extensively used in intelligent systems and fuzzy control. Most existing fuzzy reasoning methods follow rules of logical inference. In this article, fuzzy reasoning is treated as an optimization problem. The idea of optimal fuzzy reasoning is reviewed and three new optimal fuzzy reasoning methods are given by using new optimization objective functions. The robustness of fuzzy reasoning, that is, how errors in premises affect conclusions in fuzzy reasoning, is evaluated in a probabilistic or statistical context by using the Monte Carlo simulation method. Six optimal fuzzy reasoning methods are evaluated in comparison with the CRI method in terms of probabilistic robustness.