From fuzzy regression to gradual regression: Interval-based analysis and extensions

Autor: Sylvie Galichet, Reda Boukezzoula, Didier Coquin
Přispěvatelé: Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])
Rok vydání: 2018
Předmět:
Information Systems and Management
Intervals and Gradual Intervals
02 engineering and technology
01 natural sciences
Theoretical Computer Science
Interval arithmetic
010104 statistics & probability
Fuzzy regression
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG]
Artificial Intelligence
Statistics
0202 electrical engineering
electronic engineering
information engineering
[INFO]Computer Science [cs]
0101 mathematics
Regression problems
Parametric statistics
Mathematics
Possibility and Belief Function Theories
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Regression
Computer Science Applications
Ontic and Epistemic visions
Formalism (philosophy of mathematics)
[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT]
Control and Systems Engineering
Possibilistic and Least-Squares Regressions
Imprecision and Uncertainty
Ontic
020201 artificial intelligence & image processing
Gradual Regression
Software
Zdroj: Information Sciences
Information Sciences, Elsevier, 2018, 441, pp. 18-40. ⟨10.1016/j.ins.2018.02.002⟩
ISSN: 0020-0255
DOI: 10.1016/j.ins.2018.02.002
Popis: This paper proposes an analysis of parametric interval-based regression methodologies according to ontic and epistemic visions of intervals. When assuming an epistemic point of view, a new interpretation of fuzzy regression through the notion of gradual intervals is developed, which leads to gradual regression. Gradual regression is viewed as an extension of the imprecise interval-based regression, which is obtained by integrating an uncertain dimension. Gradual intervals can yield improved specificity compared to conventional intervals and jointly consider the concepts of imprecision and uncertainty through a single and coherent formalism. The formulation of the gradual regression problem, its resolution and the propagation of the information through the obtained regressive models are carried out via gradual interval arithmetic. The proposed method allows not only the extension of the interval vision to the gradual case but also interesting interpretations according to non-additive confidence measure theories (possibility and belief functions).
Databáze: OpenAIRE
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