A fuzzy logic system based on Schweizer-Sklar t-norm

Based on the Schweizer-Sklar t-norm, a fuzzy logic system UL* is established, and its soundness theorem and completeness theorem are proved. The following facts are pointed out: the well-known formal system SBL∼ is a semantic extension of UL*; the fuzzy logic system IMTLΔ is a special case of UL* when two negations in UL* coincide. Moreover, the connections between the system UL* and some fuzzy logic formal systems are investigated. Finally, starting from the concepts of “the strength of an ‘AND’ operator” by R.R. Yager and “the strength of fuzzy rule interaction” by T. Whalen, the essential meaning of a parameter p in UL* is explained and the use of fuzzy logic system UL* in approximate reasoning is presented.