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In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T(briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and T-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm T(in short, T-fuzzy ideal) is a T-fuzzy subalgebra but the converse does not generally hold. As in T-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the T-fuzzy ideals are proved.

In this paper, we define the right Boolean lifting property (left Boolean lifting property) RBLP (LBLP) for pseudo BL-algebra to be the property that all Boolean elements can be lifted modulo every right filter (left filter) and next we study the behavior of RBLP (LBLP) with respect to direct products of pseudo BL-algebra. We introduce some conditions, which turn out to be a strengthening and a weakling of RBLP (LBLP) respectively and which open new ways of approaching the study of the RBLP (LBLP) in pseudo BL-algebras.

AbstractIn this paper, we introduce the notion of hesitant fuzzy (implicative) filters and get some results on BE- algebras and show that every hesitant fuzzy implicative filter is a hesitant fuzzy filter but not the converse. Finally, we state and prove the relationship between hesitant fuzzy (implicative) filters and γ-inclusive sets.

In this paper, we introduce the notion of anti fuzzy filter and study the $$\mathcal{N }$$ N -subalgebra(filter) of $$CI$$ CI -algebra $$X$$ X . We prove that every anti fuzzy filter of $$BE$$ BE -algebra is an anti fuzzy subalgebra, but it is not valid in $$CI$$ CI -algebra. Finally, the notion of fuzzy translations and fuzzy extension of anti fuzzy filter in $$CI$$ CI -algebras are introduced. We show that every anti fuzzy filter can be as an anti fuzzy extension, but converse may not be true in general.

As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras, the operations may be partially well defined and the axioms partially true or, respectively, totally outer-defined and the axioms totally false. These NeutroAlgebras and AntiAlgebras form a new field of research, which is inspired from our real world. In this paper, we study neutrosophic quadruple algebraic structures and NeutroQuadrupleAlgebraicStructures. NeutroQuadrupleGroup is studied in particular and several examples are provided. It is shown that (NQ(Z),÷)is a NeutroQuadrupleGroup. Substructures of NeutroQuadrupleGroups are also presented with examples.