FUZZY p-IDEALS IN MV-ALGEBRAS

Abstract

In this paper, we introduce the notion of p-ideals of MV-algebras and characterization of p-ideals is given.  Also, we show that p-ideals equivalent to Boolean ideals in MV-algebras.  In addition, we introduce the notion of fuzzy p-ideals of an MV-algebra and show that in any MV-algebra, the concept of fuzzy p-ideals is equivalent to fuzzy Boolean ideals and fuzzy implicative ideals.  Also, several characterizations of these fuzzy ideals are given and prove that extension theorem of fuzzy p-ideals.  Furthermore, we describe the transfer principle for fuzzy p-ideals in terms of level subsets.  Finally, by using the notions of maximal and normal fuzzy p-ideals, we show that under certain conditions a fuzzy p-ideal is two valued and takes the values 0 and 1.