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Advances in Fuzzy Systems
Volume 2008, Article ID 586893, 9 pages
Research Article

Fuzzy Boundary and Fuzzy Semiboundary

M. Athar1 and B. Ahmad1,2

1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
2Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Kingdom of Saudi Arabia

Received 29 September 2007; Revised 3 February 2008; Accepted 21 April 2008

Academic Editor: Eyke Hüllermeier

Copyright © 2008 M. Athar and B. Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzzy-semiderived) sets.