ON THE INTEGRAL-REPRESENTATION OF FUZZY POSSIBILITY MEASURES

The integral representations of fuzzy possibility measures using the S hilkret and Sugeno integrals are discussed. In the case of the Shilkre t integral, it is shown that each fuzzy possibility measure p has a Pi -a.e. unique integral representation by a Markov kernel K, where Pi, i s a possibility measure induced by p. For the Sugeno integral, conditi ons ensuring the uniqueness of Radon-Nikodym-like derivatives of max-m easures are given. As a corollary we obtain the conditions for the uni queness of the Sugeno integral representation of fuzzy possibility mea sures using extended Pi-Markov kernels. For non-extended Markov kernel s, the Sugeno integral representation of a fuzzy possibility measure p is Pi-a.e. unique if and only if the induced possibility measure Pi i s trivial. The sigma-decomposability of possibility measures is discus sed.