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arXiv · 1501.00326

Decomposition approaches to integration without a measure

Salvatore Greco·Radko Mesiar·Fabio Rindone·Ladislav Sipeky
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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.

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Salvatore Greco, Radko Mesiar, Fabio Rindone, Ladislav Sipeky. 2015-01-01. Decomposition approaches to integration without a measure. https://arxiv.org/abs/1501.00326

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