Abstract
Correct expressions of the reverse and α-reverse triple I methods for fuzzy reasoning are established in new manners. Aiming at the existing different formulas of the reverse and α-reverse triple I methods based on Łukasiewicz implication I L , we discuss their relations and correct some of them. Further, the α-reverse triple I method is extended to a new form, called α(u,v)-reverse triple I method, which can contain the reverse triple I method as its particular case. This is another improved point to the existing formulas.
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References
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Systems Man and Cybernetics 3(1), 28–44 (1973)
Wang, G.J.: Fully implicational triple I method for fuzzy reasoning (in Chinese). Science in China (Series E) 29(1), 43–53 (1999)
Pei, D.W.: Two triple I methods for FMT problem and their reductivity (in Chinese). Fuzzy Systems and Mathematics 15(4), 1–7 (2001)
Pei, D.W.: Full implication triple I algorithms and their consistency in fuzzy reasoning. Journal of Mathematical Research and Exposition 24, 359–368 (2004)
Song, S., Feng, C., Lee, E.S.: Triple I method of fuzzy reasoning. Computer and Mathematics with Applications 44, 1567–1579 (2002)
Wang, G.J., Fu, L.: Unified forms of triple I method. Computers and Mathematics with Applications 49, 923–932 (2005)
Liu, H.W., Wang, G.J.: Unified forms of fully implicational restriction methods for fuzzy reasoning. Information Sciences 177(3), 956–966 (2007)
Liu, H.W., Wang, G.J.: Triple I method based on pointwise sustaining degrees. Computers and Mathematics with Applications 55, 2680–2688 (2008)
Wang, G.J.: Non-classical Mathematical Logic and Approximate Reasoning. Science in China Press, Beijing (2003)
Wang, G.J., Liu, H.W., Song, J.S.: A survey of triple I method– its origin, development, application and logical versions. Fuzzy System and Mathematics 20(6), 1–14 (2006)
Song, S.J., Wu, C.: Reverse triple I method of fuzzy reasoning. Science in China (Series E) 32(2), 230–246 (2002)
Fodor, J.C.: Contrapositive symmetry of fuzzy implications. Fuzzy Sets and Systems 69, 141–156 (1995)
Zhao, Z., Li, Y.: Reverse triple I method of fuzzy reasoning for the implication operator R L . Computers and Mathematics with Applications 53(7), 1020–1028 (2007)
Peng, J., Hou, J., Li, H.: Reverse triple I methods based on several common implications. Advance of Natural Sciences 15(4), 404–409 (2005)
Qin, K.Y., Pei, Z.: Opposite direction triple I method under Łukasiewicz implication operator. Fuzzy Systems and Mathematics 19(2), 1–5 (2005)
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Liu, Hw. (2009). The Correct Expressions of Reverse Triple I Methods for Fuzzy Reasoning. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_158
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DOI: https://doi.org/10.1007/978-3-642-03664-4_158
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03663-7
Online ISBN: 978-3-642-03664-4
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