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Information SciencesVolume 630, June 2023, Pages 252-270

Choquet type integrals for single-valued functions with respect to set-functions and set-multifunctions(Article)

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  • aCollege of Mathematics, Changchun Normal University, Jilin, Changchun, 130032, China
  • bFaculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, 81005, Slovakia
  • cPalacky University, Olomouc, 17. listopadu 12, Olomouc, 77146, Czech Republic
  • dSingidunum University, Danijelova 29, Belgrade, 11000, Serbia

Abstract

Due to their numerous applications such as in decision making, information fusion, game theory, and data mining, Choquet integrals have recently attracted much attention. In this study, two generalization types of Choquet integrals are presented. First, a generalized Choquet type integral of a single-valued function is introduced with respect to a set-function and measure. Several of its properties, such as convergence theorems and Jensen's inequality, are proved. Second, in the spirit of the single-valued Choquet integral, a generalized Choquet type set-valued integral for a single-valued function with respect to a set-multifunction and measure is introduced using Aumann integrals as well as various properties, including convergence theorems. © 2023 Elsevier Inc.

Author keywords

Choquet integralChoquet type integralConvergence theoremFuzzy measureSet-functionSet-multifunction

Indexed keywords

Engineering controlled terms:Data miningDecision makingDecision theoryIntegral equationsSet theory
Engineering uncontrolled termsChoquetChoquet integralChoquet type integralConvergence theoremFuzzy measuresMulti-functionsPropertySet functionSet-multifunctionSingle valued functions
Engineering main heading:Game theory

Funding details

Funding sponsor Funding number Acronym
6524105,IGAPRF2022017
Natural Science Foundation of Jilin Province222614JC0106101856,APVV-18-0052
National Natural Science Foundation of China11271062NSFC
Science Fund of the Republic of Serbia

  • 1

    The present study was funded by the National Natural Science Foundation of China (No. 11271062 ) and the Natural Science Foundation of Jilin Province (No. 222614JC0106101856 ) (for the first author), by grant APVV-18-0052 and by the IGA project of the Faculty of Science Palacký University Olomouc IGAPRF2022017 (for the second author) as well as by the project on Artificial Intelligence ATLAS (grant No. 6524105 ) funded by Science Fund of the Republic Serbia (for the third author).

  • ISSN: 00200255
  • CODEN: ISIJB
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1016/j.ins.2023.02.038
  • Document Type: Article
  • Publisher: Elsevier Inc.

  Zhang, D.; College of Mathematics, Changchun Normal University, Jilin, Changchun, China;
© Copyright 2023 Elsevier B.V., All rights reserved.

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