Using the Interval Metric for Modeling Entities Geometrics in R2 – Case Study Interval Circumference

Authors

DOI:

https://doi.org/10.5540/tema.2020.021.01.65

Keywords:

Intervalar, intervalar distance, intervalar circumference, pixels

Abstract

The study of some distances provide science away to separate two entities.It has applications in various fields such as remote sensing, datamining, pattern recognition and multivariate data analysis and others. If the distance is a Hausdorff metric, the guarantee is that all individuals are available. With the use of the distance of Trindade et al, we intend to extend the real topology to an interval topology, since the interval distance preserves the uncertainties and exits noise in the data. The present work proposes an interval circumference using an interval distance of a point to the center (pixel), like a set of pixels obeying certain distances to the center. With the interval circumference we intend to extend the notion of open ball and the concepts of neighborhood for the construction of the interval topology. A circumference separates a space into three regions, inner region, border region and outer region, where we construct our notion of neighborhood. In this work we will explore only the geometric properties of the intervalcircumference, we will extrapolate the notion from point to pixel by providing a differentiated frontier region for the clustering area.

Author Biographies

Sergio S. Aguiar, State University of Southwest of Bahia

Department of Exact and Technological Sciences

Roque M. P. Trindade, State University of Southwest of Bahia

Department of Exact and Technological Sciences

Alexsandra O. Andrade, State University of Southwest of Bahia

Department of Exact and Technological Sciences

Alzira F. Silva, State University of Southwest of Bahia

Department of Exact and Technological Sciences

Gonçalo R. Cerquiera, State University of Southwest of Bahia

Department of Exact and Technological Sciences

References

A. K. Bhunia and S. S. Samanta. A study of interval metric and its application in multi-objective optimization with interval objectives. Computers & Industrial Engineering,74:169-178, 2014.

R.E. Moore. Interval Analisys. 1966.

R. M. P.Trindade, B. R. C. Bedregal, A. D. D.Neto, and B. M. Acioly. New advanced technology, chapter An interval metric, pages 147-156. Kluwer Academic Publishers:Norwell, 2010.

Fabiana T. Santana. Uma Fundamentação para Sinais e Sistemas Intervalares. PhD Thesis,Universidade Federal do Rio Grande do Norte, 2011.

F.T. Santana, F.L.de Santana, A.D. Dória Neto, and R.H.N. Santiago. Sinais e sistemas definidos sobre aritmética intervalar complexa. TEMA, 13:85-96, 2012.

A. Takahashi, A.D. Dória Neto, and B.R.C Bedregal. An introduction interval kernel-based methods applied on support vector machines.

Adriana Takahashi. Máquina de Vetor-Suporte Intervalar (Vector-support machine interval). PhDThesis, Universidade Federal do Rio Grande do Norte, 2012.

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Published

2020-03-27

How to Cite

Aguiar, S. S., Trindade, R. M. P., Andrade, A. O., Silva, A. F., & Cerquiera, G. R. (2020). Using the Interval Metric for Modeling Entities Geometrics in R2 – Case Study Interval Circumference. Trends in Computational and Applied Mathematics, 21(1), 65. https://doi.org/10.5540/tema.2020.021.01.65

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Original Article