Limit properties of quasi-arithmetic means

  • Authors:
  • Anna Kolesáarová

  • Affiliations:
  • Faculty of Chemical Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2001

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Abstract

Limit properties of the class {Mgλ}λ ∈(0, ∞) of all quasi-arithmetic means generated by λ-powers of a given generator g are studied. Special types of generators of quasi-arithmetic means that uniquely correspond to the additive generators of continuous Archimedean t-norms or t-conorms are considered. It is shown that for λ → ∞, the situation is similar to that for t-norms and t-conorms [6]. For λ → 0+, the limit operators are quasi-geometric means. Finally, the limit properties of the class {Mgα}λ ∈(0, ∞) of all quasi-arithmetic means generated by functions gα, gα(x) = g(xα) are investigated.