Generalizing expected values to the case of L *-fuzzy events

0545170 - ÚTIA 2022 RIV GB eng J - Článek v odborném periodiku
Klement, E.P. - Kouchakinejad, F. - Guha, D. - Mesiar, Radko
Generalizing expected values to the case of L *-fuzzy events.
International Journal of General Systems. Roč. 50, č. 1 (2021), s. 36-62. ISSN 0308-1079. E-ISSN 1563-5104
Institucionální podpora: RVO:67985556
Klíčová slova: fuzzy event * capacity * Choquet integral * comonotone additivity * comonotone maxitivity * Expected value * linearity * Sugeno integral
Obor OECD: Pure mathematics
Impakt faktor: 2.435, rok: 2021
Způsob publikování: Open access
http://library.utia.cas.cz/separaty/2021/E/mesiar-0545170.pdf https://www.tandfonline.com/doi/full/10.1080/03081079.2020.1870459

Starting with [Goguen, J.A. 1967. Journal of Mathematical Analysis and Applications], several generalizations of the original definition of a fuzzy set have been proposed. In one popular case, one considers as truth values the points in the lower left triangle of the unit square, where their first coordinate is interpreted as “degree of membership”, and their second coordinate as “degree of non-membership”. Generalizing ideas in [Zadeh, L.A. 1968. Journal of Mathematical Analysis and Applications], [Grzegorzewski, P. and E. Mrówka. 2002. In: Soft Methods in Probability, Statistics and Data Analysis, Heidelberg: Physica], [Grzegorzewski, P. 2013. Information Sciences] and [Klement, E.P. and R. Mesiar. 2015. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems], the concept of expected values (based on capacities) of fuzzy events in this general sense is introduced and investigated. Expected values satisfying additional properties such as positive-linearity, comonotone additivity and comonotone maxitivity are studied, as well as an extension to real-valued expected values.
Trvalý link: http://hdl.handle.net/11104/0321919