International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21-24, Pages 1239-1253
doi:10.1155/S0161171204306186
Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras
Jianming Zhan
, Dajing Xiang
and Zhisong Tan
Department of Mathematics, Hubei Institute for Nationalities, Hubei Province, Enshi 445000, China
Abstract
We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy multiply positive implicative hyper BCK-ideal. Moreover, we introduce the notions of Noetherian hyper BCK-algebras and hyper homomorphisms of hyper BCK-algebras and investigate some related properties. Finally, we introduce the concept of hyper normalization of hyper BCK-algebras and discuss related properties.