Affiliations: [a] Department of Mathematics, Islamic Azad University Central Tehran Branch, Tehran, Iran
| [b] Department of Mathematics, Shahid Beheshti University, Tehran, Iran
Correspondence:
[*]
Corresponding author. R.A. Borzooei, Department of Mathematics, Shahid Beheshti University, Tehran, Iran. Tel.:
+989124903982; Fax:+982122431652; E-mail: [email protected].
Abstract: The aim of this paper is to introduce the notions of fuzzy filters, fuzzy (positive) implicative filters and fuzzy fantastic filters in pseudo hoops and investigate some of their properties. Some characterizations of fuzzy filters and fuzzy implicative filters are derived. The relation among these fuzzy filters are investigated and it is proved that any fuzzy fantastic and fuzzy positive implicative filter is a fuzzy implicative filter. Finally, we define a congruence relation by fuzzy filters on pseudo hoops and prove that if μ is a fuzzy normal implicative filter or fuzzy positive implicative filter, then A/μ is a Boolean algebra.
