Crisp and Fuzzy Topological Interior and Closure Operators with Inclusion Degree. Theory and Applications

  • Authors:

  • Homa Fashandi;James F. Peters

  • Affiliations:

  • Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6 Canada. {fashandi, jfpeters}@ee.umanitoba.ca;Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6 Canada. {fashandi, jfpeters}@ee.umanitoba.ca

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2013

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Abstract

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a means of dealing with imperfections and small errors, especially in cases such as digital images where boundaries of subsets of an image are not crisp. The properties of the new operators are presented. Applications of the proposed operators are given in terms of rough sets and mathematical morphology.