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Variable Differently Implicational Inference for R- and S-Implications

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  • Yiming Tang

    (Information and Communication Engineering, Postdoctoral Research Station, School of Computer and Information, Hefei University of Technology, Heifei 230009, China2AnHui Province Key Laboratory of Affective, Computing and Advanced Intelligent Machine, Hefei University of Technology, Hefei 230009, China)

  • Fuji Ren

    (Institute of Technology and Science, The University of Tokushima, Minami Josanjima, Tokushima 770-8506, Japan)

Abstract

As a generalization of the compositional rule of inference (CRI) algorithm and the fully implicational algorithm, the differently implicational algorithm of fuzzy inference not only inherit the advantages of the fully implicational algorithm, but also has stronger practicability. Then, the variable differently implicational algorithm was proposed to make the current differently implicational algorithms compose a united whole. In this paper, the variable differently implicational algorithm is further researched focusing on the fuzzy modus tollens (FMT) problem. The differently implicational principle for FMT is improved. Moreover, the unified solutions of the variable differently implicational algorithm for FMT are accomplished for R- and S-implications. Following that, as an important index of fuzzy inference, the continuity of this algorithm is analyzed for main R- and S-implications, in which excellent performance is obtained. Finally, its optimal solutions as well as inference examples are provided for several specific R- and S-implications.

Suggested Citation

  • Yiming Tang & Fuji Ren, 2016. "Variable Differently Implicational Inference for R- and S-Implications," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1235-1264, September.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:05:n:s0219622016500334
    DOI: 10.1142/S0219622016500334
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    References listed on IDEAS

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    1. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    2. F. J. Ren, 2005. "Automatic Abstracting Important Sentences," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 141-152.
    3. Guangxu Li & Gang Kou & Changsheng Lin & Liang Xu & Yi Liao, 2015. "Multi-attribute decision making with generalized fuzzy numbers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1793-1803, November.
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