Fully implicational methods for interval-valued fuzzy reasoning with multi-antecedent rules

Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-antecedent rules which are called triple I method, hierarchical triple I method and URC triple I method respectively. At the same time, we analyze the Modus-Ponens (MP for short) and continuity properties of these methods and investigate the equivalence between the first method and the latter two methods. We also restrict our discussion to Zadeh fuzzy set theory and obtain a series of corresponding results.