Abstract
In our work we show that the operations of interval algebra can be expressed by morphological operations on an appropriately chosen lattice defined over the set of intervals on the real line, when regarding real interval arithmetic, and in the complex plane, when regarding complex interval arithmetic. Using the morphological representation of the interval operations, a generalization of the additive interval operations over the family of compact convex sets in Rn is considered.
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References
Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
Heijmans, H. J. A. M.: Morphological Image Operators, Academic Press, Boston, 1994.
Kreinovich, V., Nesterov, V. M., and Zheludeva, N. A.: Interval Methods That Are Guaranteed to Underestimate (and the Resulting New Justification of Kaucher Arithmetic), Reliable Computing 2(2) (1996), pp. 119–124.
Markov, S. M.: Extended Interval Arithmetic, Compt. Rend. Acad. Bulg. Sci. 30(9) (1977), pp. 1239–1242.
Markov, S. M.: Some Applications of the Extended Interval Arithmetic to Interval Iterations, Computing Suppl. 2 (1980), pp. 69–84.
Markov, S. M.: Extended Interval Arithmetic Involving Infinite Intervals, Mathematica Balkanica, New series 6 (1992), pp. 269–304.
Markov, S. M.: On the Algebra of Intervals and Convex Bodies, J. UCS (1997), to appear.
Matheron, G.: Random Sets and Integral Geometry, Wiley, New York, 1975.
Serra, J.: Image Analysis and Mathematical Morphology, Academic Press, London, 1982.
Serra, J.: Mathematical Morphology for Complete Lattices, in: Serra, J. (ed.), Image Analysis and Mathematical Morphology, Vol.2, Academic Press, London, 1988.
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Popov, A.T. A Relation Between Morphological and Interval Operations. Reliable Computing 4, 167–178 (1998). https://doi.org/10.1023/A:1009985126164
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DOI: https://doi.org/10.1023/A:1009985126164