Abstract: In this paper, we give a method of similarity measure between the elements of vague sets. 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 rule and that in the consequent of rule. We also give a method of approximate reasoning based on similarity measure between the elements of vague sets. When the membership functions of vague set are discrete functions, after giving one-to-one mapping between the universe of discourse of fuzzy terms in the antecedent of rule and that in the consequent of rule, we present a method of linear interpolation into the true/false membership functions of the vague sets for the antecedent of rule and fact, converting them into continuous functions. Finally, we provide a method of approximate reasoning based on similarity measure between the elements of vague sets.

Key words: Vague set, true/false membership function, approximate reasoning, similarity measure between elements