A comparative study on similarity-based fuzzy reasoning methods

If the given fact for an antecedent in a fuzzy production rule (FPR) does not match exactly with the antecedent of the rule, the consequent can still be drawn by technique such as fuzzy reasoning. Many existing fuzzy reasoning methods are based on Zadeh's Compositional Rule of Inference (CRI) which requires setting up a fuzzy relation between the antecedent and the consequent part. There are some other fuzzy reasoning methods which do not use Zadeh's CRI. Among them, the similarity-based fuzzy reasoning methods, which make use of the degree of similarity between a given fact and the antecedent of the rule to draw the conclusion, are well known. In this paper, six similarity-based fuzzy reasoning methods are compared and analyzed. Two of them are newly proposed by the authors. The comparisons are two-fold. One is to compare the six reasoning methods in drawing appropriate conclusions for a given set of FPRs. The other is to compare them based on five issues: 1) types of FPR handled by these methods; 2) the complexity of the methods; 3) the accuracy of the conclusion drawn; 4) the accuracy of the similarity measure; and 5) the multi-level reasoning capability. The results have shed some lights on how to select an appropriate fuzzy reasoning method under different environments.