Decomposition approaches to integration without a measure

0457408 - ÚTIA 2017 RIV NL eng J - Journal Article
Greco, S. - Mesiar, Radko - Rindone, F. - Sipeky, L.
Decomposition approaches to integration without a measure.
Fuzzy Sets and Systems. Roč. 287, č. 1 (2016), s. 37-47. ISSN 0165-0114. E-ISSN 1872-6801
Institutional support: RVO:67985556
Keywords : Choquet integral * Decision making * Decomposition integral
Subject RIV: BA - General Mathematics
Impact factor: 2.718, year: 2016
http://library.utia.cas.cz/separaty/2016/E/mesiar-0457408.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0258928