Some notes on optimal fuzzy reasoning methods

Abstract

The optimal fuzzy reasoning (OFR) method proposed by Zhang and Cai (2004) is treated as a control problem and it is dramatically different from other existing fuzzy reasoning methods. The aim of this paper is to make some notes on OFR methods. We give a modification of an OFR method presented by Zhang and Cai. Some advantages and limitations of OFR methods are examined. We introduce several new OFR methods based on the Łukasiewicz implication, the Kleene-Dienes implication and the Zadeh implication. The reasoning consistency of the proposed methods is studied. The relationship between the OFR method and other fuzzy reasoning methods (e.g., the compositional rule of inference method and the pointwise optimizing fuzzy inference method) is examined.