Mathematical model constraction and application to data analysis using nonlinear integral with respect to nonadditive measure

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K05003
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: Honda Aoi 九州工業大学, 大学院情報工学研究院, 准教授 (50271119)
• 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)
• Research Collaborator: JAMES Simon Deakin University, Lecturer
• Project Period (FY): 2015-04-01 – 2018-03-31
• 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

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.

Free Research Field

応用数学