Espaços vetoriais e topológicos de intervalos generalizados com alguns conceitos de cálculo e otimização intervalar
This work presents a method to endow the generalized interval set M = I(R) ∪ I(R); where I(R) = f[a1; a2] : a1 a2 and a1; a2 2 Rg and I(R) = f[a1; a2] : [a2; a1] 2 I(R)g; with some different structures, such as algebraic, topological, and metric. We also equip M with order relations. Actually, we di...
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| Format: | doctoral thesis |
| Status: | Published version |
| Publication Date: | 2014 |
| Country: | Brasil |
| Institution: | Universidade Estadual Paulista (UNESP) |
| Repository: | Repositório Institucional da UNESP |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.unesp.br:11449/110603 |
| Online Access: | http://hdl.handle.net/11449/110603 |
| Access Level: | Open access |
| Keyword: | Álgebra linear Espaços topologicos Espaços vetoriais Otimização matematica Topological spaces |
| Summary: | This work presents a method to endow the generalized interval set M = I(R) ∪ I(R); where I(R) = f[a1; a2] : a1 a2 and a1; a2 2 Rg and I(R) = f[a1; a2] : [a2; a1] 2 I(R)g; with some different structures, such as algebraic, topological, and metric. We also equip M with order relations. Actually, we did this in a more general context because we worked in Mn = M M M for n 2 N: We formulated interval optimization problems and related them to classic multi-objective optimization problems. We presented a version of the mini-max Theorem in the interval context, and also developed concepts of calculus on the generalized interval space which are used to find the attainable state set of a classic differential inclusion under some given conditions |
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