MATCHING FUNCTION-BASED FULLY IMPLICATIONAL METHODS FOR FUZZY REASONING

New fully implicational methods for fuzzy reasoning are established based on matching functions between fuzzy sets. First, the reasoning principles are established respectively by means of the inclusion and similarity measures as the matching functions between fuzzy sets. Then, we extend them to new forms. According to these reasoning principles, we further establish a series of reasoning algorithms and analyze their properties. Some of the existing similarity-based reasoning methods turn out to be the particular cases of the new methods. We also show that the new algorithms are continuous if and only if they are consistent under certain conditions.