Abstract
This article presents the first self-contained and direct proof of a widely recognized result that the discrete Choquet integral, when defined from a discrete fuzzy measure (or capacity), is convex if and only if the discrete fuzzy measure itself is submodular. In contrast to existing proofs, our argument is constructed directly from the fuzzy measure defined on a finite set, employing only standard techniques from the theory of capacities and Choquet integration.
(Communicated by Anatolij Dvurečenskij)
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© 2025 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- A new categorical equivalence for stone algebras
- On special classes of prime filters in BL-algebras
- A note on characterized and statistically characterized subgroups of 𝕋 = ℝ/ℤ
- New Young-type integral inequalities using composition schemes
- The structure of pseudo-n-uninorms with continuous underlying functions
- Jensen-type inequalities for a second-order differential inequality condition
- A direct proof of the characterization of the convexity of the discrete Choquet integral
- Envelope of plurifinely plurisubharmonic functions and complex Monge-Ampère type equation
- Fekete-Szegö inequalities for Φ-parametric and β-spirllike mappings of complex order in ℂn
- Entire function sharing two values partially with its derivative and a conjecture of Li and Yang
- Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation
- Weighted B-summability and positive linear operators
- Some properties and applications of convolution algebras
- On measures of σ-noncompactess in F-spaces
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- Intermediately trimmed sums of oppenheim expansions: A strong law
- Novel weighted distribution: Properties, applications and web-tool
- On the q-Gamma distribution: Properties and inference
- Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
- Prof. RNDr. Anatolij Dvurečenskij, DrSc. 75th anniversary