Fuzzy Filters of Hoops Based on Fuzzy Points - Mona Aaly Kologani; Mohammad Mohseni Takallo; Hee Sik Kim (Mathematics, 2019)
In this paper, we define the concepts of <semantics> ( ∈ , ∈ ) </semantics> and <semantics> ( ∈ , ∈ ∨ q ) </semantics> -fuzzy filters of hoops, discuss some properties, and find some equivalent definitions of them. We define a congruence relation on hoops by an <semantics> ( ∈ , ∈ ) </semantics> -fuzzy filter and show that the quotient structure of this relation is a hoop.