Abstract
In the basic models of fuzzy reasoning, the fuzzy propositions are the same type of fuzzy sets. In the paper, we intend to investigate the inference mechanisms of mixed fuzzy reasoning for asymmetric types such that the fuzzy propositions are the different type of fuzzy sets. We establish the two new models for the asymmetric type approximate reasoning problems and present the corresponding methods to solve the new models. Furthermore, we analyze the characterizations of the solutions and give their reductivity.
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References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 3, 28–44 (1973)
Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice Hall PTR, Upper Saddle River (1997)
Wang, G.J.: Non-classical Mathematical Logic and Approximate Reasoning, 2nd edn. Science Press, Beijing (2008). (in Chinese)
Wang, G.J.: Full implicational triple I method for fuzzy reasoning. Sci. China Ser. E 29(1), 43–53 (1999)
Pei, D.W.: Unified full implication algorithms of fuzzy reasoning. Inf. Sci. 178(2), 520–530 (2008)
Liu, H.W., Wang, G.J.: Unified forms of fully implicational restriction methods for fuzzy reasoning. Inf. Sci. 177, 956–966 (2007)
Wang, G.J., Duan, J.Y.: On robustness of the full implication triple I inference method with respect to finer measurements. Int. J. Approx. Reason. 55, 787–796 (2014)
Tang, Y.M., Liu, X.P.: Differently implicational universal triple I method of (1,2,2) type. Comput. Math. Appl. 59, 1965–1984 (2010)
Tang, Y.M., Yang, X.Z.: Symmetric implicational method of fuzzy reasoning. Int. J. Approx. Reason. 54, 1034–1048 (2013)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication inintuitionistic fuzzy and interval-valued fuzzy set theory: construction. classification, application. Int. J. Approx. Reason. 35, 55–95 (2004)
Zheng, M.C., Shi, Z.K., Liu, Y.: Triple I method of approximate reasoning on Atanassov’s intuitionistic fuzzy sets. Int. J. Approx. Reason. 55, 1369–1382 (2014)
Liu, Y., Zheng, M.C.: The Dual Triple I Methods of FMT and IFMT. Math. Prob. Eng. 2014, Article ID 507401, 8 (2014). doi:10.1155/2014/507401
Zheng, M.C., Shi, Z.K., Liu, Y.: Triple I method of intuitionistic fuzzy reasoning based on residual implicator. Sci. China Inf. Sci. 43, 810–820 (2013). (in Chinese)
Acknowledgments
The authors acknowledge their supports from the National Natural Science Foundation of China (Nos. 11401361, 61473336, 61572016).
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Liu, Y., Zheng, MC. (2017). Mechanisms of Mixed Fuzzy Reasoning for Asymmetric Types. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_29
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DOI: https://doi.org/10.1007/978-3-319-46206-6_29
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