Mathematical model constraction and application to data analysis using nonlinear integral with respect to nonadditive measure
| Project/Area Number |
15K05003
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyushu Institute of Technology |
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Principal Investigator |
Honda Aoi 九州工業大学, 大学院情報工学研究院, 准教授 (50271119)
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| Co-Investigator(Kenkyū-buntansha) |
乃美 正哉 九州工業大学, 大学院情報工学研究院, 講師 (50208302)
大木 真 熊本高等専門学校, 情報通信エレクトロニクス工学科, 准教授 (10624562)
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| Research Collaborator |
JAMES Simon Deakin University, Lecturer
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 非線形積分 / 非加法的測度 / 多変量データ解析 / 数理モデル / Lp空間 / 多変量解析 / 主観的評価問題 / 包除積分 / 非加法的積分 |
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| Outline of Final Research Achievements |
We have obtained several results on constraction of mathematical model and application to data analysis using inclusion-exclusion integral, nonlinear integral with respect to nonadditive measure in these three years. We have given a method of construction of mathematical model and interpreting of decision process to the objective variables described by the model. Moreover, we have given sufficient conditions of nonadditive measures and interaction operators used to define the integral for monotonicity of the integral. We have discussed linearity and topology of Lp-space determined by nonlinear integrals. We have also partially succesed generalization of the definition to nondescrete nonadditive measure space.
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Report
(4 results)
Research Products
(36 results)
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[Presentation] 包除積分の非離散化2017
Author(s)
本田あおい,岡崎悦明
Organizer
日本数学会年会
Place of Presentation
首都大学東京（東京都八王子市）
Year and Date
2017-03-24
Related Report
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[Presentation] Inclusion-exclusion integral2015
Author(s)
Aoi Honda, Yoshiaki Okazaki
Organizer
12th International Conference on Modeling Decisions for Articial Intelligence
Place of Presentation
Skovde, Sweden
Year and Date
2015-09-21
Related Report
Int'l Joint Research
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