Journal
FUZZY SETS AND SYSTEMS
Volume 281, Issue -, Pages 88-102Publisher
ELSEVIER
DOI: 10.1016/j.fss.2015.07.010
Keywords
Monotone measure; Choquet integral; Shilkret integral; Sugeno integral; Universal integral; Decomposition integral
Funding
- Upper Austrian Government [Wi-2013-168051/WWin/Kai]
- National Natural Science Foundation of China [11371332]
- European Regional Development Fund in the IT4Innovations Centre of Excellence project [CZ.1.05/1.1.00/02.0070]
- MPNS [174009]
- Provincial Secretariat for Science and Technological Development of Vojvodina
- [VEGA 1/0420/15]
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An overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set (called here monotone measures). Our survey includes not onlythe Choquet integral (1954) [10], the Shilkret integral (1971) [66] and the Sugeno integral (1974) [71] and some of their properties, but also some more general and more recent concepts as universal integrals Klement etal. (2010) [27] and decomposition integrals Even (2014) [13], together with some of their properties, such as integral inequalities and convergence theorems. (C) 2015 Elsevier B.V. All rights reserved.
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