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| A fuzzy logic system based on Schweizer-Sklar t-norm | |
| 摘 要： | In recent years, the basic research of fuzzy logic and fuzzy reasoning is growing ac- tively day by day, such as the basic logic system BL proposed by Hajek[1]; fuzzy logic system MTL proposed by Esteva and Godo[2]; fuzzy reasoning, implication operators … |
| 收稿时间： | 2004-12-30 |
| 修稿时间： | 2005-08-30 |
A fuzzy logic system based on Schweizer-Sklar t-norm |
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| ZHANG Xiaohong,HE Huacan,XU Yang. A fuzzy logic system based on Schweizer-Sklar t-norm[J]. Science in China(Information Sciences), 2006, 49(2): 175-188. DOI: 10.1007/s11432-006-0175-y | |
| Authors: | ZHANG Xiaohong HE Huacan XU Yang |
| Affiliation: | 1. Faculty of Science, Ningbo University, Ningbo 315211, China;School of Computer Science, Northwestern Polytechnical University, Xi'an 710072, China 2. School of Computer Science, Northwestern Polytechnical University, Xi'an 710072, China 3. Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China |
| Abstract: | 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. |
| Keywords: | t-norm fuzzy logic system UL* completeness UL*-algebras approximate reasoning. |
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