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Approximate Fuzzy Continuity of Functions

Approximate Fuzzy Continuity of Functions

Mark Burgin, Oktay Duman
Copyright: © 2011 |Volume: 1 |Issue: 4 |Pages: 10
ISSN: 2156-177X|EISSN: 2156-1761|EISBN13: 9781613507087|DOI: 10.4018/ijfsa.2011100103
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MLA

Burgin, Mark, and Oktay Duman. "Approximate Fuzzy Continuity of Functions." IJFSA vol.1, no.4 2011: pp.37-46. http://doi.org/10.4018/ijfsa.2011100103

APA

Burgin, M. & Duman, O. (2011). Approximate Fuzzy Continuity of Functions. International Journal of Fuzzy System Applications (IJFSA), 1(4), 37-46. http://doi.org/10.4018/ijfsa.2011100103

Chicago

Burgin, Mark, and Oktay Duman. "Approximate Fuzzy Continuity of Functions," International Journal of Fuzzy System Applications (IJFSA) 1, no.4: 37-46. http://doi.org/10.4018/ijfsa.2011100103

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Abstract

The conventional continuity of a function was further advanced by the concept of approximate continuity introduced by Denjoy to solve some problems of differentiation and integration. According to this new type of continuity, the (classical) continuity conditions may be true not necessarily everywhere, but almost everywhere with respect to some measure, e.g., Borel measure or Lebesgue measure. However, functions that come from real life sources, such as measurement and computation, do not allow, in a general case, to test whether they are continuous or even approximately continuous in the strict mathematical sense. Hence, in this paper, the authors overcome these limitations by introducing and studying the more realistic concept of the approximate fuzzy continuity of functions.

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