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R. A. Borzooei,M. Sabetkish,E. H. Roh,M. Aaly Kologani 한국지능시스템학회 2019 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.19 No.3
In this paper, we introduce the notion of int-soft filters in hoops and related properties are investigated. Characterizations of int-soft filters are discussed and we introduce a congruence relation by using int-soft filter and we show that the quotient is a hoop. Also, we introduce the notions of int-soft n-fold (positive) implicative and int-soft n-fold fantastic filters of hoops, we study some equivalence definitions of them and the relation between them, we prove that every int-soft n-fold positive implicative filter is an int-soft fantastic filter and int-soft implicative filter. Also, we investigate about the quotient structure that is made by them.