A Fuzzy Logic with Similarity

Fuzzy sets and fuzzy logic are important and practical mathematical tools for processing uncertain and vague information, and similarity is a fundamental relation in fuzzy sets In order to integrate the similarity relation into fuzzy logic, a fuzzy logic with similarity is proposed and its syntax and semantics are given Some properties of fuzzy inference based on the resolution principle and paramodulation are discussed First, the significance of fuzzy logical inference by the resolution principle is discussed in the context of fuzzy first order logic Second, it is shown that the fuzzy logical inference by the paramodulation is always significant Finally, considering that many problem solving systems are based on reductio ad absurdum, the completeness of the resolution and paramodulation is proved for fuzzy predicate calculus