Fuzzy n-fold fantastic filters on hoop algebras

Document Type : Original Article


Department of Mathematics, Zarrin Dasht Branch, Islamic Azad university, Zarrin Dasht, Iran


In this paper, first we introduce the concept of fuzzy n-fold positive implicative filters on hoop algebras and study some of properties. Next we define and study fuzzy n-fold fantastic filters on hoop algebras. Also, the relationship between  fuzzy n-fold positive implicative filter and some other fuzzy filters likeness fuzzy n-fold implicative filter and fuzzy n-fold  fantastic filters are investigated for example every fuzzy n-fold implicative filter is a fuzzy n-fold positive implicative filter  on hoop algebras. Then we obtain some condition equivalent with fuzzy n-fold fantastic filters and every fuzzy filter on  chain hoop algebra is a fuzzy n-fold fantastic filter. Finally we show that the quotient of fuzzy n-fold fantastic filters is a  Boolean algebra. 


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