Extended gradual interval (EGI) arithmetic and its application to gradual weighted averages
| Autor: | Reda Boukezzoula, Moheb Elmasry, Sylvie Galichet, Laurent Foulloy |
|---|---|
| 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: | 2014 |
| Předmět: |
Discrete mathematics
Logic [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] Subtraction Inverse Context (language use) 010103 numerical & computational mathematics 02 engineering and technology Interval (mathematics) Division (mathematics) 01 natural sciences Fuzzy logic Artificial Intelligence 0202 electrical engineering electronic engineering information engineering [INFO]Computer Science [cs] 020201 artificial intelligence & image processing Multiplication 0101 mathematics Arithmetic Representation (mathematics) Mathematics |
| Zdroj: | Fuzzy Sets and Systems Fuzzy Sets and Systems, Elsevier, 2014, 257, pp. 67-84. ⟨10.1016/j.fss.2013.08.003⟩ |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2013.08.003 |
| Popis: | International audience; We combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval (EGI) arithmetic in which subtraction and division operators are the inverse operators of addition and multiplication, respectively. Use of the proposed EGI operators can lead to non-monotonic gradual intervals that are not fuzzy subsets and cannot be represented by fuzzy intervals. In this context and when fuzzy representation results are desired, an approximation strategy is proposed to determine the nearest fuzzy interval of the non-monotonic gradual interval obtained. This approximation is viewed as an interval regression problem according to an optimization procedure. The EGI operators are applied to the common fuzzy weighted average (FWA) leading to a gradual weighted average (GWA). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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