Additive generators of associative functions

@article{Vicenk2005AdditiveGO,
  title={Additive generators of associative functions},
  author={Peter Vicen{\'i}k},
  journal={Fuzzy Sets and Systems},
  year={2005},
  volume={153},
  pages={137-160}
}
Associativity of a two place functionT (x, y) = f (−1)(f (x) + f (y)) wheref : [0,1] → [0,∞] is a strictly monotone function and f (−1) : [0,∞] → [0,1] is the pseudo-inverse of f depends only on properties of the range of f. The following question is answered: what property of the range of an additive generator f is necessary and sufficient for associativity of the corresponding generated function T? We also introduce the characterization of all additive generatorsf of Twith propertyT (. . . T… CONTINUE READING

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