@Article{BarbieriNavaraWeberSCJ03,
  IS = { zkontrolovano 07 Dec 2003 },
  UPDATE  = { 2003-12-03 },
  author =      {Barbieri, Giuseppina and Navara, Mirko and Weber, Hans},
  title =       {Characterization of {T}-measures},
  authorship =  {33-33-33},
  journal =     {Soft Computing},
  publisher =   {Springer},
  address =     {Berlin,Germany},
  issn =        {1432-7643},
  year =        {2003},
  volume =      {8},
  pages =       {44-50},
  month =       {October},
  number =      {1},
  importance =  {1},
  project =     {MSM 212300013, GACR 201/02/1540},
  psurl       = {[PDF]},
  annote = {As a natural generalization of a measure space, Butnariu
    and Klement introduced T-tribes of fuzzy sets with T-measures.
    They made the first steps towards a characterization of monotonic
    real-valued T-measures for a Frank triangular norm T. Later
    on, Mesiar and the authors of this paper found independently two
    generalizations, one for vector-valued T-measures with respect
    to Frank t-norms (in particular for nonmonotonic ones), the other
    for monotonic real-valued T-measures with respect to general
    strict t-norms. Here we present a common generalization---a
    characterization of nonmonotonic T-measures with respect to an
    arbitrary strict t-norm. Moreover, we prove this for vector-valued
    T-measures. Using their characterization, we generalize Ljapunov
    Theorem to this context.  },
  keywords =    {fuzzy set, triangular norm, fuzzy measure, 
                 T-measure, tribe, Ljapunov Theorem},
}