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Δ-Choquet integral on time scales with applications

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  • Negi, Shekhar Singh
  • Torra, Vicenç

Abstract

The fundamental purpose of this work is to analyze Δ-Choquet integrals on time scales which is a special case of Choquet integral on abstract fuzzy (non-additive) measure space. We first present a Δ-Choquet integral with respect to non-additive Δ-measure or more precisely a distorted Lebesgue Δ-measure on an arbitrary time scale. Consequently, we come up with a more general integral than the standard Choquet integral of continuous and discrete calculus. Its use can be seen as convenient in economics, decision making, artificial intelligence, and many more. Particularly, in economics, most of the models are dynamic models (continuous and/or discrete), and those can be easily studied on time scales. Further, some basic essential results and properties of the general integral are studied. For instance, we discuss translation, homogeneity, linearity, and many more with respect to the functions and measures of the integral.

Suggested Citation

  • Negi, Shekhar Singh & Torra, Vicenç, 2022. "Δ-Choquet integral on time scales with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001795
    DOI: 10.1016/j.chaos.2022.111969
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    References listed on IDEAS

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    8. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
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