×

Gradual inference rules in approximate reasoning. (English) Zbl 0736.68070

Summary: Gradual inference rules of the form “The more \(X\) is \(F\), the more \(Y\) is \(G\) (or of similar forms with “the less” instead of “the more”), which express a progressive change of the degree to which the entity \(Y\) satisfies the gradual property \(G\) when the degree to which the entity \(X\) satisfies the gradual property \(F\) is modified, are often encountered in commonsense reasoning. A representation of such rules by means of fuzzy sets is proposed and discussed. This representation turns out to be based on a special implication function already considered in multiple- valued logic. Patterns of reasoning involving gradual inference rules are formalized. Their links with interpolation mechanisms are pointed out.

MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B52 Fuzzy logic; logic of vagueness
68T30 Knowledge representation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bruxelles, S.; Raccah, P. Y., Information et argumentation: l’expression de la conséquence, (Actes Conférence “Cognitiva”, CESTA, Paris, Vol. 1 (18-22 May, 1987)), 445-452
[2] Buisson, J. C.; Farreny, H.; Prade, H., Dealing with imprecision and uncertainty in the expert system DIABETO-III (in French), (Proc. 2nd Int. Conf. on Artificial Intelligence, CIIAM-86. Proc. 2nd Int. Conf. on Artificial Intelligence, CIIAM-86, Marseille, Hermès, Paris (1986)), 705-721
[3] Buisson, J. C.; Prade, H., Un système d’inférence pratiquant l’interpolation au moyen de règles à prédicats graduels—une application au calcul des rations caloriques, (Actes Convention Intelligence Artificielle 88-89 (23-27 Jan. 1989), Hermès: Hermès Paris), 43-57
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic: Academic New York · Zbl 0444.94049
[5] Dubois, D.; Prade, H., Towards the analysis and the synthesis of fuzzy mappings, (Yager, R. R., Fuzzy Set and Possibility Theory—Recent Developments (1982), Pergamon: Pergamon New York), 316-326
[6] Dubois, D.; Prade, H., On distances between fuzzy points and their use for plausible reasoning, (Proc. IEEE Int. Conf. on Cybernetics and Society. Proc. IEEE Int. Conf. on Cybernetics and Society, Bombay-New Delhi (30 Dec. 1983-7 Jan. 1984)), 300-303
[7] Dubois, D.; Prade, H., Fuzzy logics and the generalized modus ponens revisited, Cybernet. Syst., 15, 293-331 (1984) · Zbl 0595.03016
[8] Dubois, D.; Prade, H., A theorem on implication functions defined from triangular norms, Stochastica, VIII, 3, 267-279 (1984) · Zbl 0581.03016
[9] Dubois, D.; Prade, H.; de Farreny, H.; Martin-Clouaire, R.; Testemale, C., Possibility Theory — An Approach to Computerized Processing of Uncertainty (1988), Plenum: Plenum New York, (French editions, Masson, Paris 1985 and 1987). · Zbl 0703.68004
[10] Dubois, D.; Prade, H., A typology of fuzzy “If… then…” rules, (Proc. 3rd Inter. Fuzzy Systems Association Congress. Proc. 3rd Inter. Fuzzy Systems Association Congress, Seattle, Wash. (6-11 Aug. 1989)), 782-785
[11] Eshragh, F.; Mamdani, E. H., A general approach to linguistic approximation, Int. J. Man-Machine Stud., 11, 501-519 (1979) · Zbl 0403.68075
[12] Farreny, H.; Prade, H., Uncertainty handling and fuzzy logic control in navigation problems, (Hertzberger, L. O.; Groen, F. C.A., Preprints, Int. Conf. on Intelligent Autonomous Systems. Preprints, Int. Conf. on Intelligent Autonomous Systems, Amsterdam, The Netherlands, 1986 (1987), North-Holland), 218-225, Proc.
[13] Gaines, B. R., Foundations of fuzzy reasoning, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 19-75 · Zbl 0342.68056
[14] Goguen, J. A., Concept representation in natural and artificial languages: axioms, extensions and applications for fuzzy sets, Int. J. Man-Machine Stud., 6, 513-561 (1974) · Zbl 0321.68055
[15] Lebailly, J.; Martin-Clouaire, R.; Prade, H., Use of fuzzy logic in a rule-based system in petroleum geology, (Sanchez, E.; Zadeh, L. A., Approximate Reasoning in Intelligent Systems, Decision and Control (1987), Pergamon: Pergamon New York), 125-144
[16] Mizumoto, M., Fuzzy inference using max-Λ composition in the compositional rule of inference, (Gupta, M. M.; Sanchez, E., Approximate Reasoning in Decision Making (1982), North-Holland: North-Holland Amsterdam), 67-76 · Zbl 0503.94032
[17] Mizumoto, M.; Fukami, S.; Tanaka, K., Some methods of fuzzy reasoning, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 117-136
[18] Negoita, C. V.; Ralescu, D. A., Applications of Fuzzy Sets to Systems Analysis (1975), Birkhäuser: Birkhäuser Basel · Zbl 0326.94002
[19] Pedrycz, W., On generalized fuzzy relation equations and their applications, J. Math. Anal. Appl., 107, 520-536 (1985) · Zbl 0581.04003
[20] Prade, H., Raisonner avec des règles d’inférence graduelle-Une approche basée sur les ensembles flous, Rev. Intell. Artif., 2, 2, 29-44 (1988)
[21] Sanchez, E., Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic, (Gupta, M. M.; Saridis, G. N.; Gaines, B. R., Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland Amsterdam), 221-234
[22] Sugeno, M.; Nishida, M., Fuzzy control of model car, Fuzzy Sets Syst., 16, 103-113 (1985)
[23] Trillas, E.; Valverde, L., On mode and implication in approximate reasoning, (Gupta, M. M.; Kandel, A.; Bandler, W.; Kiszka, J. B., Approximate Reasoning in Expert Systems (1985), North-Holland: North-Holland Amsterdam), 157-166
[24] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606
[25] Zadeh, L. A., A fuzzy set-theoretic interpretation of linguistic hedges, J. Cybernet., 2, 3, 4-34 (1972)
[26] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 3-28 (1978) · Zbl 0377.04002
[27] Zadeh, L. A., QSA/FL-qualitative systems analysis based on fuzzy logic (1989), University of California: University of California Berkeley
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.