Fuzzy Positive Implicative Filters of Hoops Based on Fuzzy Points

Abstract

In this paper, we introduce the notions of (is an element of,is an element of)-fuzzy positive implicative filters and (is an element of,is an element of boolean OR q)-fuzzy positive implicative filters in hoops and investigate their properties. We also define some equivalent definitions of them, and then we use the congruence relation on hoop defined in blue [Aaly Kologani, M.; Mohseni Takallo, M.; Kim, H.S. Fuzzy filters of hoops based on fuzzy points. Mathematics. 2019, 7, 430; doi:10.3390/math7050430] by using an (is an element of,is an element of)-fuzzy filter in hoop. We show that the quotient structure of this relation is a Brouwerian semilattice.