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In this paper, we define the concepts of <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mo>&#8712;</mo> <mo>,</mo> <mo>&#8712;</mo> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mo>&#8712;</mo> <mo>,</mo> <mo>&#8712;</mo> <mo>&or;</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-fuzzy filters of hoops, discuss some properties, and find some equivalent definitions of them. We define a congruence relation on hoops by an <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mo>&#8712;</mo> <mo>,</mo> <mo>&#8712;</mo> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-fuzzy filter and show that the quotient structure of this relation is a hoop.