×

zbMATH — the first resource for mathematics

Strict Archimedean \(t\)-norms and \(t\)-conorms as universal approximators. (English) Zbl 0955.68108
Summary: In knowledge representation, when we have to use logical connectives, various continuous \(t\)-norms and \(t\)-conorms are used. In this paper, we show that every continuous \(t\)-norm and \(t\)-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean \(t\)-norm (\(t\)-conorm).

MSC:
68T30 Knowledge representation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Klir, G.; Yuan, B., Fuzzy sets and fuzzy logic: theory and applications, (1995), Prentice-Hall Englewood Cliffs, NJ · Zbl 0915.03001
[2] Nguyen, H.T.; Walker, E.A., A first course in fuzzy logic, (1997), CRC Press Boca Raton, Florida · Zbl 0856.03019
[3] Shortliffe, E.H., Computer-based medical consultation: MYCIN, (1976), Elsevier Amsterdam
[4] Buchanan, B.G.; Shortliffe, E.H., Rule-based expert systems. the MYCIN experiments of the Stanford heuristic programming project, (1984), Addison-Wesley Reading, MA
[5] Smith, M.H.; Kreinovich, V., Optimal strategy of switching reasoning methods in fuzzy control, (), 117-146, ch. 6 · Zbl 0897.93036
[6] Ling, C.H., Representation of associative functions, Publ. math. debrecen, 12, 189-212, (1965) · Zbl 0137.26401
[7] Schweizer, B.; Sklar, A., Associative functions and abstracts semigroups, Publ. math. debrecen, 10, 69-81, (1963) · Zbl 0119.14001
[8] Jenei, S., Limit theorems and the family of nilpotent ordinal sums, (), 110-114
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.