This paper proposes a fuzzy-inference method in which fuzzy sets are defined by the families of their a-level sets, based on the resolution identity theorem. This method stands in contrast to the conventional fuzzy-inference method, in which fuzzy sets are defined by membership functions. It has the following advantages over cohventional methods: (1) it studies the characteristics of fuzzy inference, in particular the input-output relations of fuzzy inference; (2) it provides fast inference operations and requires less memory capacity for fuzzy sets defined in universes of discourse with a large number of elements; (3) it easily interfaces with two-valued logic; and (4) it effectively matches with systems that include fuzzy-set operations based on the extension principle.This paper first compares fuzzy sets defined by the families of their a-level sets with those defined by membership functions in terms of processing time and required memory capacity in fuzzy logic operations. It then derives the fuzzy-inference method and proves important propositions of fuzzy-inference operations. It also presents some examples of inference operations by the proposed method, and considers fuzzy-inference characteristics and computational efficiency from a-level-set-based fuzzy inference. This paper finally concludes with a brief discussion. (b) Fig. 1. Fuzzy-set definitions (the symbol " " shows an element in the discrete space *Yd). (a) Fuzzy-set definition by a membership function. (b)Fuzzy-set definition by the family of n-level sets.