Homotopia Intervalar

Eduardo Silva Palmeira, Benjamín René Callejas Bedregal, Regivan Hugo Nunes Santiago

Abstract


Nesse trabalho apresentamos uma formalização do conceito matemático de homotopia mergulhado no ambiente das funções intervalares definidas sobre o conjunto dos intervalos com extremos reais I(R), tanto considerando a Scottcontinuidade quanto a Moore-continuidade. Definimos o que é uma homotopia Scott intervalar, bem como o que é uma homotopia Moore intervalar. Em seguida mostramos que esses dois conceitos coincidem para representações canônicas. Para finalizar, mostramos alguns resultados envolvendo homotopia intervalar e conceitos relacionados, tais como composição de homotopias e retrato por deformação.

References


[2] B.R.C. Bedregal, A. Takahashi, The best interval representation of T-norms and automorphisms, Fuzzy Sets and Systems, 157, No. 24 (2006), 3220–3230.

[3] J.C. Burkill, Functions of intervals, Proceedings of the London Mathematical Society, 375–446, (1924).

[4] J. Dugundji, “Topology”, Allyn and Bacon Inc., Boston, 1966.

[5] P.S. Dwyer, “Computation with Approximate Numbers”, p. 11–34, Wiley and Sons, New York, 1951.

[6] L. Jaulin, M. Kieffer, O. Didrit, E. Walter “Applied Interval Analysis”, Springer-Verlag, London, 2001.

[7] R.E. Moore, “Automatic Error Analysis in Digital Computation”, Technical Report LMSD-4842, Lockheed Missiles and Space Division, Sunnyvale, California, 1959.

[8] R.E. Moore, “Interval Analysis”, Prentice-Hall, Englewood Cliffs, NJ, 1966.

[9] R.E. Moore, R.B. Kearfott, M.J. Cloud,“Interval Analysis”, Society for Industrial and Applied Mathematics, PA, 2009.

[10] J.R. Munkres, “Topology, a First Course”, Prentice Hall, Englewood Cliffs, NJ, 1975.

[11] J. Piper, Interval Skeletons, In “Proceedings 11th IAPR Internacional Conference on Pattern Recognition”, vol. III, 1992.

[12] R.H.N. Santiago, B.C. Bedregal, B.M. Acióly, Comparing continuity of interval functions based on Moore and Scott topologies, Eletronic Journal on Mathematics of Computation (2005), disponível em http://www.cin.ufpe.br/ejmc.

[13] R.H.N. Santiago, B.C. Bedregal, B.M. Acióly, Formal aspects of correctness and optimality of interval computations, Formal Aspects of Computing, 18 (2006), 231–243.

[14] T. Sunaga, Theory of an interval algebra and its application to numerical analysis, RAAG Memoirs, 2 (1958), 547–564.

[15] W. Taylor, Simple equations on real intervals, Algebra Univers., 61 (2009), 213–226.

[16] G.W. Whitehead, “Elements of Homotopy theory”, Springer-Verlag, NY, 1978.

[17] M. Warmus, “Calculus of Approximations”, Bull. Acad. Polon. Sci. Cl. III, 4 (1956), 463–464.

[18] R.C. Young, The algebra of many-valued quantities, Math. Ann., (1931), 260–290.




DOI: https://doi.org/10.5540/tema.2011.012.02.0145

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia