1. Decomposition approaches to integration without a measure
- Author
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Greco, Salvatore, Mesiar, Radko, Rindone, Fabio, and Sipeky, Ladislav
- Subjects
Mathematics - Functional Analysis - Abstract
Extending the idea of Even and Lehrer [3], 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 [3] and also covers problems of linear programming and combinatorial optimization. Finally, we introduce some new types of integrals related to optimization tasks., Comment: 15 pages
- Published
- 2015