Double set-function Choquet integral with applications(Article)
- aCollege of Mathematics, Changchun Normal University, Changchun, 130032, China
- bFaculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, 81005, Slovakia
- cUniversity of Ostrava, 30. dubna 22, Ostrava 1, 70103, Czech Republic
- dSingidunum University, Danijelova 29, Belgrade, 11000, Serbia
Abstract
Related to many applications in different fields, such as game theory, information fusion, data mining, and decision making, we have introduced in one our previous paper so called generalized Choquet-type integral for a real-valued function concerning a set-function and a σ-additive measure. The present study further generalizes the generalized Choquet-type integral in terms of a double set-function Choquet integral for a real-valued function based on a set-function and fuzzy measure. Several of its properties and convergence theorems are obtained, and a novel type of Jensen's inequality is proved. The stability of the proposed system formed by a double set-function Choquet integral concerning multiple inputs and one output is indicated. An effective application in decision making is shown through numerical examples. © 2024
Indexed keywords
| Engineering controlled terms: | Data miningDecision theoryFrequency modulationFuzzy systemsGame theoryIntegral equationsSet theory |
|---|---|
| Engineering uncontrolled terms | Choquet integralConvergence theoremCumulative prospect theoryDouble set-function choquet integralDouble setsFuzzy measureFuzzy measuresSet function |
| Engineering main heading: | Decision making |
Funding details
| Funding sponsor | Funding number | Acronym |
|---|---|---|
| Changchun Normal University | CNU | |
| Natural Science Foundation of Jilin Province | 20230101182JC | |
| National Natural Science Foundation of China | 12371455 | NSFC |
| Vedecká Grantová Agentúra MŠVVaŠ SR a SAV | 1/0036/23 | VEGA |
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1
The authors would like to thank the unknown referees, the Area Editor and Professor Witold Pedrycz, Editor-in-Chief, for their very valuable comments and suggestions. This work was supported by the Natural Science Foundation of Jilin Province (No.20230101182JC) and the National Natural Science Foundation of China (No.12371455) (for the 1st author), by grant VEGA 1/0036/23 (for the 2nd author) as well as by Agreement on Engaging Foreign Experts for Scientific Research Cooperation Changchun Normal University (China) (for the 3rd author).
- ISSN: 00200255
- CODEN: ISIJB
- Source Type: Journal
- Original language: English
- DOI: 10.1016/j.ins.2024.120948
- Document Type: Article
- Publisher: Elsevier Inc.
Zhang, D.; College of Mathematics, Changchun Normal University, Changchun, China;
© Copyright 2024 Elsevier B.V., All rights reserved.
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