On maxitive integration

Cattaneo, Marco E. G. V.

Abstract

A functional is said to be maxitive if it commutes with the (pointwise) supremum operation. Such functionals find application in particular in decision theory and related fields. In the present paper, maxitive functionals are characterized as integrals with respect to maxitive measures (also known as possibility measures or idempotent measures). These maxitive integrals are then compared with the usual additive and nonadditive integrals on the basis of some important properties, such as convexity, subadditivity, and the law of iterated expectations.

Citation

Cattaneo, M. E. G. V. (2016). On maxitive integration. Fuzzy Sets and Systems, 304, 65-81. https://doi.org/10.1016/j.fss.2016.02.008

• Journal Article Type: Article
• Acceptance Date: Feb 8, 2016
• Online Publication Date: Feb 11, 2016
• Publication Date: Dec 1, 2016
• Deposit Date: Mar 23, 2016
• Publicly Available Date: Feb 12, 2018
• Journal: Fuzzy sets and systems
• Print ISSN: 0165-0114
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 304
• Pages: 65-81
• DOI: https://doi.org/10.1016/j.fss.2016.02.008
• Keywords: Maxitive measures; Nonadditive integrals; Choquet integral; Convexity; Subadditivity; Law of iterated expectations
• Public URL: https://hull-repository.worktribe.com/output/434038
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0165011416300252
• Additional Information: Authors' accepted manuscript of article published in: Fuzzy sets and systems, 2016, v.304.
• Contract Date: Feb 12, 2018