Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures
The aim of this paper is to generalize the Choquet-like integral with respect to a nonmonotonic fuzzy measure for generalized real-valued functions and set-valued functions, which is based on the generalized pseudo-operations and σ-⊕-measures. Furthermore, the characterization theorem and transforma...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/4631530 |
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| _version_ | 1832559104515637248 |
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| author | Ting Xie Zengtai Gong |
| author_facet | Ting Xie Zengtai Gong |
| author_sort | Ting Xie |
| collection | DOAJ |
| description | The aim of this paper is to generalize the Choquet-like integral with respect to a nonmonotonic fuzzy measure for generalized real-valued functions and set-valued functions, which is based on the generalized pseudo-operations and σ-⊕-measures. Furthermore, the characterization theorem and transformation theorem for the integral are given. Finally, we study the Lyapunov type inequality and Stolarsky type inequality for the Choquet-like integral. |
| format | Article |
| id | doaj-art-e036972c585d4343ab16c87fed87a652 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e036972c585d4343ab16c87fed87a6522025-02-03T01:30:51ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/46315304631530Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy MeasuresTing Xie0Zengtai Gong1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaThe aim of this paper is to generalize the Choquet-like integral with respect to a nonmonotonic fuzzy measure for generalized real-valued functions and set-valued functions, which is based on the generalized pseudo-operations and σ-⊕-measures. Furthermore, the characterization theorem and transformation theorem for the integral are given. Finally, we study the Lyapunov type inequality and Stolarsky type inequality for the Choquet-like integral.http://dx.doi.org/10.1155/2019/4631530 |
| spellingShingle | Ting Xie Zengtai Gong Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures Journal of Function Spaces |
| title | Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures |
| title_full | Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures |
| title_fullStr | Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures |
| title_full_unstemmed | Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures |
| title_short | Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures |
| title_sort | inequalities of lyapunov and stolarsky type for choquet like integrals with respect to nonmonotonic fuzzy measures |
| url | http://dx.doi.org/10.1155/2019/4631530 |
| work_keys_str_mv | AT tingxie inequalitiesoflyapunovandstolarskytypeforchoquetlikeintegralswithrespecttononmonotonicfuzzymeasures AT zengtaigong inequalitiesoflyapunovandstolarskytypeforchoquetlikeintegralswithrespecttononmonotonicfuzzymeasures |