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A Family I LΠGN(q,p) of Implication Operators and Triple I Methods Based on It

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Quantitative Logic and Soft Computing 2010

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 82))

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Abstract

In this paper, first, a new family T LΠGN(q,p), q ∈ [ − 1,1], P ∈ ( − ∞ , + ∞ ) of left -continuous t-norms are presented; and then its residual family I LΠGN(q,p), q ∈ [ − 1,1], P ∈ ( − ∞ , + ∞ ) of implication operators are given; finally, a generic form of Triple I methods based on the family I LΠGN(q,p) of implication operators in fuzzy reasoning is expressed.

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References

  1. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic, Lodon (1998)

    Book  MATH  Google Scholar 

  2. Zádeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zádeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cyber. 3, 28–44 (1973)

    Article  MATH  Google Scholar 

  4. Fodor, J.C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    MATH  Google Scholar 

  5. Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 313–334 (1960)

    MathSciNet  MATH  Google Scholar 

  6. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York (1983)

    MATH  Google Scholar 

  7. Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci., USA 8, 535–537 (1942)

    Article  MathSciNet  Google Scholar 

  8. Klement, E.P., Weber, S.: Generalized measures. Fuzzy Sets and Systems 40, 375–394 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Butnariu, D., Klement, E.P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions. Kluwer Academic Publishers, Dordrecht (1993)

    MATH  Google Scholar 

  10. Frank, M.J.: On the simultaneous associativity of F(x,y) and x + y − F(x,y). Aequationes Math. 19, 194–226 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, G.J.: Fully implicational triple I method for fuzzy reasoning. Sci. China (Ser. E) 29, 43–53 (1999) (in Chinese)

    MATH  Google Scholar 

  12. Wang, G.J.: Introduction to mathematical logic and resolution principle, 2nd edn. Science Press, Beijing (2009)

    Google Scholar 

  13. Pei, D.W.: Unified full implication algorithms of fuzzy reasoning. Information Sciences 178, 520–530 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jeneia, S., Montagnab, F.: Ageneral method for constructing left-continuous t-norms. Fuzzy Sets and Systems 136, 263–282 (2003)

    Article  MathSciNet  Google Scholar 

  15. Whalen, T.: Parameterized R-implications. Fuzzy sets and systems 134, 231–281 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang, X.H., He, H.C., Xu, Y.: Fuzzy logic system of based on Schweizer-Sklar T-norm. Sci. China (Ser. E) 35, 1314–1326 (2006) (in Chinese)

    MathSciNet  Google Scholar 

  17. Zhang, X.F., Meng, G.W., Zhang, A.Y.: The Families of Implication Operators and Their Application. Chinese Journal of Computers 30, 448–453 (2007) (in Chinese)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, China

    Xing-fang Zhang

Authors
  1. Xing-fang Zhang
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Editors and Affiliations

  1. Guangzhou University, Guangdong, China

    Bing-yuan Cao

  2. Shaanxi Normal University, Xi’an, China

    Guo-jun Wang

  3. Jimei University, Fujian, China

    Shui-li Chen

  4. Liaoning Technical University, Fuxing, China

    Si-zong Guo

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Zhang, Xf. (2010). A Family I LΠGN(q,p) of Implication Operators and Triple I Methods Based on It. In: Cao, By., Wang, Gj., Chen, Sl., Guo, Sz. (eds) Quantitative Logic and Soft Computing 2010. Advances in Intelligent and Soft Computing, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15660-1_14

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  • DOI: https://doi.org/10.1007/978-3-642-15660-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15659-5

  • Online ISBN: 978-3-642-15660-1

  • eBook Packages: EngineeringEngineering (R0)

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