Abstract: When the membership functions (represented by vague sets) of fuzzy terms are continuous functions, we give a one-to-one mapping between the universe of discourse of fuzzy terms in the antecedent of the rule and that in the consequent of the rule. In this way, we are able to find a method of interpolation fuzzy reasoning based on vague sets. When the membership functions of vague sets are discrete functions, after giving one-to-one mapping between the universe of discourse of fuzzy terms in the antecedent of the rule and that in the consequent of the rule, we carry out linear interpolation in the true/false membership functions of vague sets in the antecedent of the rule and fact, to turn them in to continuous functions. we are thus able to develop a method of interpolation fuzzy reasoning based on vague sets.

Key words: mapping, linear interpolation, fuzzy reasoning, Vague set