Abstract
In the process of uncertainties reasoning with universal logic, T-norm is the mathematical model of “AND” operation. T-norm and T-generator were defined on interval [0,1] in previous work. In the recent relational work, authors put forward fractional logic based on continuous radix [a, b]. This paper studied the T-norm and T-generator on any interval [a, b], discussed the two kinds of generalized T-generators: “Automorphic increase T-generator” and “Infinite decrease T-generator”. Authors found and proved the useful and important theorem: “generating theorem of generalized T-norm”. Using the integrated clusters of generalized T-norm and T-generator, authors gave the mathematical generating method for “AND” operation model of fractional logic based on any interval [a, b]. The operation model is already used to uncertainties reasoning and flexible control now.
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References
He, H.C., Wang, H., Liu, Y.H. (eds.): Universal Logics Principle. China Science Publishing House, Beijing (2001)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–357 (1965)
Hacck, S.: Deviant Logic and Fuzzy Logic, Beyond the Formalism, 2nd edn. The University of Chicago Press (1996)
Liu, L.Z., Li, K.T.: Involutive monoidal t-norm-based logic and R-0 logic. International Journal of Intelligent Systems 6, 491–497 (2004)
Esteva, F., Godo, L., Montagna, F.: Axiomatization of any residuated fuzzy logic defined by a continuous T-norm. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 172–179. Springer, Heidelberg (2003)
Hajek, P.: Observations on the monoidal t-norm logic. Fuzzy sets and system 1, 107–112 (2002)
Chen, Z.C., He, H.C., Mao, M.Y.: Approach to Fractal and Chaos Logics Based on Universal. In: 2003 Sino-Korea Symposium on Intelligent Systems, pp. 40–145 (2003)
Chen, Z.C., He, H.C., Mao, M.Y.: Correlation Reasoning of Complex System Based on Universal Logic. In: IEEE Proceedings of 2003 International Conference on Machine Learning and Cybernetics, vol. 3, pp. 1831–1835 (2003)
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Chen, Z., Mao, M., He, H., Yang, W. (2006). Generalized T-norm and Fractional “AND” Operation Model. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_85
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DOI: https://doi.org/10.1007/11795131_85
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