A refined Hölder’s inequality for Choquet expectation by Cauchy-Schwarz’s inequality
| Autor: | Hamzeh Agahi |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Information Systems and Management
Series (mathematics) Inequality media_common.quotation_subject 05 social sciences 050301 education 02 engineering and technology Measure (mathematics) Computer Science Applications Theoretical Computer Science Submodular set function Monotone polygon Choquet integral Artificial Intelligence Control and Systems Engineering Converse 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0503 education Mathematical economics Cauchy–Schwarz inequality Software Mathematics media_common |
| Zdroj: | Information Sciences. 512:929-934 |
| ISSN: | 0020-0255 |
| DOI: | 10.1016/j.ins.2019.10.010 |
| Popis: | Recently, Torra, Narukawa and Sugeno [Fuzzy Sets and Systems, 292 (2016) 364–379] obtained the Cauchy-Schwarz inequality for Choquet integral. In this paper, we first introduce a refined Holder’s inequality in Choquet calculus. Then by this inequality, we show that Cauchy-Schwarz inequality and Holder’s inequality for Choquet integral are equivalent only when the monotone measure is submodular or the integrands are comonotonic, thus closing the series of papers in this literature. Note that it is obvious that Holder’s inequality implies Cauchy-Schwarz’s inequality. But the converse is an interesting subject. This paper focuses on this subject. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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