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International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 263-270
http://dx.doi.org/10.1155/S0161171202109045

Fuzzy positive implicative ordered filters of implicative semigroups

1Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
2Department of Mathematics, Chungbuk National University, Chongju 361-763, Korea
3Department of Mathematics, Hanyang University, Seoul 133-791, Korea

Received 11 September 2001; Revised 5 May 2002

Copyright © 2002 Hindawi Publishing Corporation. 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

We consider the fuzzification of the notion of a positive implicative ordered filter in implicative semigroups. We show that every fuzzy positive implicative ordered filter is both a fuzzy ordered filter and a fuzzy implicative ordered filter. We give examples that a fuzzy (implicative) ordered filter may not be a fuzzy positive implicative ordered filter. We also state equivalent conditions of fuzzy positive implicative ordered filters. Finally, we establish an extension property for fuzzy positive implicative ordered filters.