Institute of Information Theory and Automation

Publication details

Decomposition approaches to integration without a measure

Journal Article

Greco S., Mesiar Radko, Rindone F., Sipeky L.


serial: Fuzzy Sets and Systems vol.287, 1 (2016), p. 37-47

keywords: Choquet integral, Decision making, Decomposition integral

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abstract (eng):

we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of decompositions: sub-decomposition based integrals (in economics linked with optimization problems to maximize the possible profit) and super-decomposition based integrals (linked with costs minimization). We provide several examples (both theoretical and realistic) to stress that our approach generalizes that of Even and Lehrer (2014) [3] and also covers problems of linear programming and combinatorial optimization. Finally, we introduce some new types of integrals related to optimization tasks.

RIV: BA

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Last modification: 21.12.2012
Institute of Information Theory and Automation