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Δ-Choquet integral on time scales with applications

Author

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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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    1. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
    2. Mustapha Ridaoui & Michel Grabisch, 2016. "Choquet integral calculus on a continuous support and its applications," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(1), pages 73-93.
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    5. 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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    8. Shekhar Singh Negi & Syed Abbas & Muslim Malik, 2020. "Periodic Solutions of the N-Preys and M-Predators Model with Variable Rates on Time Scales," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 945-967, September.
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    11. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
    Full references (including those not matched with items on IDEAS)

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