On the logic foundation of fuzzy reasoning. (English) Zbl 0939.03031

Summary: Fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers. Unfortunately, it seems that the two branches have not been successfully connected. The aim of this paper is to establish a so-called quasi-propositional deductive system syntactically as well as semantically, and then set a logic foundation for developing the theory of fuzzy reasoning therefrom.


03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI


[1] Y.Y. Chen, Fuzzy Control Technique and its Applications, Beijing Normal University Press, 1993
[2] Dubois, D.; Prade, H., Fuzzy sests in approximate reasoning, part 1: inference with possibility distributions, Fuzzy sets and systems, 40, 143-202, (1991) · Zbl 0722.03017
[3] Dubois, J. Lang, H. Prade, Fuzzy sests in approximate reasoning, Part 2: Logic approaches, Fuzzy sets and Systems 40 (1991) 203-244 · Zbl 0722.03018
[4] A.G. Hamilton, Logic for mathematicians, Cambridge University Press, 1978 · Zbl 0383.03003
[5] Pavelka, J., On fuzzy logic I- many-valued rules of inference, Zeitschr. f. math. logik und grundlagen d. math., 25, 45-52, (1979) · Zbl 0435.03020
[6] Pavelka, J., On fuzzy logic II - enriched residuated lattices and semantics of propositional calculi, Zeitschr. f. math. logik und grundlagen d. math., 25, 119-134, (1979) · Zbl 0446.03015
[7] Pavelka, J., On fuzzy logic III - semantic completeness of some many-valued propositional calculi, Zeitschr. f. math. logik und grundlagen d. math., 25, 447-464, (1979) · Zbl 0446.03016
[8] Zadeh, L.A., Quantative fuzzy semantics, Inform. sci., 3, 159-176, (1971) · Zbl 0218.02057
[9] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. systems man cybernet., 3, 28-44, (1973) · Zbl 0273.93002
[10] Zadeh, L.A., The concept of a linguistic variable and its applications to approximate reasoning, Inform. sci., 8, 199-249, (1975) · Zbl 0397.68071
[11] Zadeh, L.A., Why the success of fuzzy logic is not paradoxical, IEEE expert, 43-46, (1994) · Zbl 1009.03532
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.