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On computation of the compositional rule of inference under triangular norms. (English) Zbl 0782.68110
Summary: The paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under Archimedean \(t\)-norms, when both the observation and the relation parts are given by H. Hellendoorn’s [Fuzzy Sets Syst. 35, No. 2, 163-183 (1990; Zbl 0704.03006)] \(\varphi\)-function.

68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
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[1] Da, R., A critical study of widely used fuzzy implication operators and their influence on the inference rules in fuzzy expert systems, ()
[2] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[3] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE trans. automat. control, 26, 926-936, (1981)
[4] Dubois, D.; Martin-Clouarie, R.; Prade, H., Practical computing in fuzzy logic, (), 11-34
[5] Fullér, R.; Kereszfalvi, T., T-norm-based addition of fuzzy intervals, Fuzzy sets and systems, 51, 155-159, (1992)
[6] Hellendoorn, H., Closure properties of the compositional rule of inference, Fuzzy sets and systems, 35, 163-183, (1990) · Zbl 0704.03006
[7] Hellendoorn, H., The generalized modus ponens considered as a fuzzy relation, Fuzzy sets and systems, 46, 29-48, (1992) · Zbl 0773.03016
[8] Martin-Clouaire, R., Semantics and computation of the generalized modus ponens: the long paper, Internat. J. approximate reasoning, 3, 195-217, (1989) · Zbl 0689.94006
[9] Margrez, P.; Smets, P., Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems, Internal. J. intelligent systems, 4, 181-200, (1989) · Zbl 0672.03010
[10] Mizumoto, M.; Zimmermann, H.-J., Comparison of fuzzy reasoning methods, Fuzzy sets and systems, 8, 253-283, (1982) · Zbl 0501.03013
[11] Schweizer, B.; Sklar, A., Associative functions and abstract semigroups, Publ. math. debrecen, 10, 69-81, (1963) · Zbl 0119.14001
[12] Yager, R.R., Approximate reasoning as a basis for rule-based expert systems, IEEE trans. systems man cybernet., 14, 636-643, (1984) · Zbl 0555.68066
[13] Zadeh, L.A., The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy sets and systems, 11, 199-228, (1983) · Zbl 0553.68049
[14] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of linguistic variable and its applications to approximate reasoning, parts I, II, III, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[15] Zimmermann, H.-J., Fuzzy sets, decision making and expert systems, (1987), Reidel Dordrecht-Boston
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