Variable Differently Implicational Inference for R- and S-Implications

Yiming Tang and Fuji Ren
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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

International Journal of Information Technology & Decision Making (IJITDM), 2016, vol. 15, issue 05, 1235-1264

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.

Keywords: Fuzzy inference; fuzzy modus tollens; fuzzy implication; compositional rule of inference; fully implicational algorithm (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219622016500334

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