On computation of the compositional rule of inference under triangular norms.

*(English)*Zbl 0782.68110Summary: 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.

##### MSC:

68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |

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\textit{R. Fullér} and \textit{H. J. Zimmermann}, Fuzzy Sets Syst. 51, No. 3, 267--275 (1992; Zbl 0782.68110)

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##### References:

[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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