Possibility and necessity measures and integral equivalence

0477092 - ÚTIA 2018 RIV US eng J - Journal Article
Chen, T. - Mesiar, Radko - Li, J. - Stupňanová, A.
Possibility and necessity measures and integral equivalence.
International Journal of Approximate Reasoning. Roč. 86, č. 1 (2017), s. 62-72. ISSN 0888-613X. E-ISSN 1873-4731
Institutional support: RVO:67985556
Keywords : Integral equivalence * Necessity measure * Possibility measure * Survival function * Universal integral
OECD category: Statistics and probability
Impact factor: 1.766, year: 2017
http://library.utia.cas.cz/separaty/2017/E/mesiar-0477092.pdf

Integral equivalence of couples (mu, x) and (mu, y), where mu is a possibility (necessity) measure on [n] ={1,..., n} and x, y is an element of [0,1](n) is discussed and studied. We characterize the sets H(mu, x) of all y such that the couples (mu, x) and (mu, y) are integral equivalent and we add an illustrative example. Subsequently, a new characterization of possibility (necessity) measures is obtained and the coincidence of universal integrals for possibility (necessity) measures and particular vectors from [0,1](n) is shown, thus generalizing these results introduced by Dubois and Rico for the Choquet and the Sugeno integrals.
Permanent Link: http://hdl.handle.net/11104/0274030