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Aggregation operators

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Triangular Norms

Part of the book series: Trends in Logic ((TREN,volume 8))

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Abstract

Both t-norms and t-conorms are rather special operations on the unit interval [0, 1]. However, there are several other useful operations related to and/or generalizing t-norms or t-conorms, either on the unit interval or on an arbitrary closed subinterval [a, b] of the extended real line [−∞, ∞].

The interpretation of a decision as the intersection of fuzzy sets, computed by applying any t-norm based operator implies that there is no compensation between low and high degrees of membership. If, on the other hand, a decision is defined to be the union of fuzzy sets, represented by some t-conorm, full compensation is assumed. Managerial decisions hardly ever represent any of these extremes.

Hans-Jürgen Zimmermann & Paul Zysno

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© 2000 Springer Science+Business Media Dordrecht

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Klement, E.P., Mesiar, R., Pap, E. (2000). Aggregation operators. In: Triangular Norms. Trends in Logic, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9540-7_10

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  • DOI: https://doi.org/10.1007/978-94-015-9540-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5507-1

  • Online ISBN: 978-94-015-9540-7

  • eBook Packages: Springer Book Archive

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