Decomposition approaches to integration without a measure

Salvatore Greco, Radko Mesiar, Fabio Rindone, Ladislav Sipeky

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Extending the idea of Even and Lehrer (2014) [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 (2014) [3]and also covers problems of linear programming and combinatorial optimization. Finally, we introduce some new types of integrals related to optimization tasks.
Original languageEnglish
Pages (from-to)37-47
JournalFuzzy Sets and Systems
Early online date22 Jul 2015
Publication statusPublished - 1 Mar 2016


  • Decomposition integral
  • Weighting function
  • Choquet integral
  • Optimization problems
  • Decision making


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