Abstract
This paper deals with Zadeh’s compositional rule of inference [Zad73] under triangular norms: IF X is P AND X and Y have relation R, THEN Y is Q, where P and Q are fuzzy sets of the real line R, R is a fuzzy relation on R and the conclusion Q is defined via sup-T composition of P and R:
Supported by the Hungarian Research Foundation under the projects OTKA T 4281, OTKA 1/3 2152 and by the German Academic Exchange Service (DAAD).
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References
D. Dubois, R. Martin-Clouarie and H. Prade, Practical computing in fuzzy logic, In: M.M. Gupta and T. Yamakawa eds., Fuzzy Computing: Theory, Hardware, and Applications, North-Holland, Amsterdam, 1988 11–34.
M. Fedrizzi and R. Fuller, Stability in Possibilistic Linear Programming Problems with Continuous Fuzzy Number Parameters, Fuzzy Sets and Systems, 47(1992) 187–191.
R. Fullér and H.-J. Zimmermann, Computation of the Compositional Rule of Inference, Fuzzy Sets and Systems (to appear).
R. Fullér and H.-J. Zimmermann, On Zadeh’s compositional rule of inference, in: R. Lowen and M. Roubens eds., Proceedings of the Fourth IFSA Congress, Vol. Artifical Intelligence, Brussels, 1991 41–44.
H. Hellendoorn, Closure properties of the compositional rule of inference, Fuzzy Sets and Systems, 35(1990) 163–183.
O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24(1987) 301–317.
J.B. Kiszka, M.M. Gupta, P.N. Nikiforuk, Some properties of expert control systems, In: M.M. Gupta, A. Kandel and J.B. Kiszka eds., Approximate Reasoning in Expert Systems, North-Holland, Amsterdam, 1985, 283–306.
R. Martin-Clouarie, Semantics and computation of the generalized modus ponens: The long paper, International Journal of Approximate Reasoning, 3(1989) 195–217.
P. Margrez and P. Smets, Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems, International Journal of Intelligent systems, 4(1989) 181–200.
B. Schweizer and A. Sklar, Associative functions and abstract semigroups, Publ. Math. Debrecen, 10(1963) 69–81.
B. Werners, Modellierung und Aggregation Linguistischer Terme, Arbeitsbericht, No.90/03, RWTH Aachen, Institut fur Wirtschaftswissenschaften 1990.
L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man and Cybernetics, Vol.SMC-3, No.l, 1973 28–44.
L.A. Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems, 11(1983) 199–228.
H.-J. Zimmermann, Fuzzy sets, Decision Making and Expert Systems, Boston, Dordrecht, Lancaster 1987.
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© 1993 Springer Science+Business Media Dordrecht
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Fullér, R., Zimmermann, HJ. (1993). On Zadeh’s Compositional Rule of Inference. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_19
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DOI: https://doi.org/10.1007/978-94-011-2014-2_19
Publisher Name: Springer, Dordrecht
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