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Advances in Fuzzy Systems
Volume 2011, Article ID 768028, 5 pages
http://dx.doi.org/10.1155/2011/768028
Research Article

On Fuzzy Sp-Open Sets

1Department of Mathematics, Rada'a College of Education and Science, Albida, Yemen
2Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia

Received 29 December 2010; Accepted 18 February 2011

Academic Editor: Ibrahim Ozkan

Copyright © 2011 Hakeem A. Othman. 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.

Abstract

A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzy sp-open sets, are introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets we discussed. Moreover, we introduce the fuzzy sp-continuous (resp., fuzzy sp-open) mapping and other stronger forms of sp-continuous (resp., fuzzy sp-open) mapping and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mapping and introduce fuzzy sp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.