Δ-Choquet integral on time scales with applications

Shekhar Singh Negi and Vicenç Torra

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

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.

Keywords: Lebesgue measure; Distorted Lebesgue measure; Time-scale; Lebesgue Δ-measure; Lebesgue Δ-integral; Lebesgue-Stieltjes Δ-measure; Lebesgue-Stieltjes Δ-integral; Choquet integral; Fuzzy measure (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001795

DOI: 10.1016/j.chaos.2022.111969

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