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The (fuzzy) filter of the Sheffer stroke Hilbert algebra was addressed by Oner, Katican and Borumand Saeid. The weak version of the filter was discussed by Jun and Oner. In this manuscipt, with the fuzzy version of the weak filter in mind, the notions of fuzzy weak filters and (∈, ∈ ∨q)-fuzzy weak filters are introduced, and their properties are explored. Conditions under which t-level set, Qt-set and t-∈ ∨q-set become weak filters are explored in relation to fuzzy weak filters and (∈, ∈ ∨q)-fuzzy weak filters. The relationship and characterization of the fuzzy weak filter and the (∈, ∈ ∨q)-fuzzy weak filter are investigated.

In this paper, we introduced the concept of a soft hoop and we investigated some of their properties. Then, we established different types of intersections and unions of the family of soft hoops. We defined two operations ⊙ and → on the set of all soft hoops and we proved that with these operations, it is a hoop and also is a Heyting algebra. Finally we introduced a congruence relation on the set of all soft hoops and we investigated the quotient of it.

In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.

In this paper, we introduce a new algebra, called a BI-algebra, which is a generalization of a (dual) implication algebra and we discuss the basic properties of BI-algebras, and investigate ideals and congruence relations.

The purpose of this paper is to initiate the concept of n-dimensional (∈γ, ∈γ, ∨qδ)-fuzzy subalgebra in BRK-algebra and investigate some of their related properties. We also show that the relationship between n-dimensional (∈γ, ∈γ, ∨qδ)-fuzzy subalgebra and the crisp subalgebra in BRK-algebra are discussed.