Decomposition approaches to integration without a measure
Functional Analysis
2015-01-05 v1
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.
Cite
@article{arxiv.1501.00326,
title = {Decomposition approaches to integration without a measure},
author = {Salvatore Greco and Radko Mesiar and Fabio Rindone and Ladislav Sipeky},
journal= {arXiv preprint arXiv:1501.00326},
year = {2015}
}
Comments
15 pages