International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 263-270
doi:10.1155/S0161171202109045
Fuzzy positive implicative ordered filters of implicative semigroups
Young Bae Jun1
, Young Hee Kim2
and Hee Sik Kim3
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
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.