Research on Four Type-2 Fuzzy Reasoning Models
The previous discussion about type-2 fuzzy reasoning mechanisms just paid attentions to Mamdani models based on Mamdani implication operator. There is no doubt that the operator is justifiable, since such an operator possesses characteristic clipping effect, i.e. limiting the consequence membership function with the truth value of the antecedent. However, Mamdani implication operator does not uphold classical logic, i.e. it is in no agreement with the classic binary interpretation of implication. All of the Kleene-Dienes operator, Lukasiewicz operator, Zadeh operator and Reichenbach operator, which derive from equivalencies of the classic binary implication, have in common the feature of generalizing classic logic. This paper investigates type-2 fuzzy reasoning models and algorithms based on these four implication operators, respectively. In the view upholding classical logic, proposed models and algorithms seem to be more natural than of the Mamdani type.
Helen Zhang, Gang Shen and David Jin
Y. J. Zhang et al., "Research on Four Type-2 Fuzzy Reasoning Models", Advanced Materials Research, Vols. 204-210, pp. 406-411, 2011