Abstract
The integral representations of fuzzy possibility measures using the Shilkret and Sugeno integrals are discussed. In the case of the Shilkret integral, it is shown that each fuzzy possibility measure p has a Π-a.e. unique integral representation by a Markov kernel !, where Π is a possibility measure induced by p. For the Sugeno integral, conditions ensuring the uniqueness of Radon-Nikodym-like derivatives of max-measures are given. As a corollary we obtain the conditions for the uniqueness of the Sugeno integral representation of fuzzy possibility measures using extended Π -Markov kernels. For non-extended Markov kernels, the Sugeno integral representation of a fuzzy possibility measure p is Π-a.e. unique if and only if the induced possibility measure Π is trivial. The σ-decomposability of possibility measures is discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
