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  2015, Vol. 28 Issue (2): 97-104    DOI: 10.16451/j.cnki.issn1003-6059.201502001
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Three Kinds of Fuzzy Modus Tollens and Algorithms Based on Different Fuzzy Negations
PAN Zheng-Hua, ZHAO Jie-Xin, WANG Shan-Shan
Institute of Mathematics and Physics, School of Science, Jiangnan University, Wuxi 214122

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Abstract  

Fuzzy modus tollens (FMT) is one of the most basic inference forms in fuzzy reasoning. As a premise of FMT, fuzzy negation plays a major role in inference. In this paper, based on the fuzzy propositional logic with contradictory negation, opposite negation and medium negation (FLCOM), contradictory negation, opposite negation and medium negation are proved to be different fuzzy negations, and thus three kinds of fuzzy modus tollens, FMT1, FMT2 and FMT3, are proposed,which are different from FMT respectively based on contradictory negation, opposite negation and medium negation. Furthermore, based on the R-implication operator IR, a fuzzy NR-implication operator INR is defined which is associated with IR. The algorithms of FMT1, FMT2 and FMT3 are proposed according to the algorithm of FMT, and it is proved that algorithms of FMT1, FMT2 and FMT3 are reducible algorithms when I ≤INR.

Key wordsFuzzy Modus Tollens(FMT)      Contradictory Negation      Opposite Negation      Medium Negation      Algorithm of Fuzzy Modus Tollens     
Received: 27 September 2013     
ZTFLH: TP181  
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PAN Zheng-Hua
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WANG Shan-Shan
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PAN Zheng-Hua,ZHAO Jie-Xin,WANG Shan-Shan. Three Kinds of Fuzzy Modus Tollens and Algorithms Based on Different Fuzzy Negations[J]. , 2015, 28(2): 97-104.
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http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.201502001      OR     http://manu46.magtech.com.cn/Jweb_prai/EN/Y2015/V28/I2/97
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