Universal Implication Operators: Properties and Applications

The aim of this paper is exploring the properties and applications of universal implication operators which were proposed by Prof. H.C. He in 2001. Firstly, fourteen properties which are very important to the studies of implication operators are listed. Three mutually independent properties which can infer the fourteen properties are obtained. Secondly, the properties of universal implication operators are given. Thirdly, the applications of universal implication operators in fuzzy reasoning and fuzzy control are discussed. The universal implication inference engine is proposed, and the errors of three fuzzy systems in drawing two-dimensional and three-dimensional surfaces are compared. We obtain that the fuzzy system include universal implication inference engine has the smallest errors under the same fuzzy rules