A representation of a comonotone-x∨-additive and monotone functional by two Sugeno integrals

Authors:
Endre Pap;Biljana P. Mihailović
Affiliations:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia and Montenegro;Faculty of Engineering, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia and Montenegro
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

There is obtained a representation of a comonotone-@?@?-additive, weak @?@?-homogeneous and monotone functional L (defined on the class of functions on finite set) as a symmetric maximum of two Sugeno integrals. This representation is a generalization of certain previous results, which are useful for cumulative prospect theory. As a consequence of a result on general fuzzy rank and sign-dependent functionals considered on functions defined on the infinitely countable basic set X it is obtained that the symmetric Sugeno integral is comonotone-@?@?-additive functional on the class of functions with finite support.