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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.

A new structure, so called soju structure, is introduced by combining intuitionistic fuzzy set and soft set, which is applied to BCK/BCI-algebras. The notions of soju subalgebra and soju ideal in BCK/BCI-algebras are introduced, and related properties are investigated. A strong soju subalgebra in BCI-algebras is introduced, and a condition for a soju subalgebra to be strong is provided. Relations between soju subalgebra and soju ideal are discussed, and conditions for a soju structure to be a soju ideal in a BCK-algebra are considered. Characterizations of soju subalgebra and soju ideal are considered, and the homomorphic image and preimage of soju subalgebra is discussed. [ABSTRACT FROM AUTHOR]

In this article, we further study the filter theory of semihoops. Moreover, we use the prime (maximal) filters to construct the prime (maximal) spectrum on semihoops, and prove that the prime spectrum is a compact T0{T}_{0} topological space and that the maximal spectrum is a compact T2{T}_{2} topological space. As an application, in order to study the relationship between the spectrum of semihoops and the spectrum of lattices, we introduce the reticulations of semihoops and obtain some related results.

The new definitions of intuitionistic from magnified translation fuzzy in AT-subalgebra and AT-ideals on AT-algebras study the relationships between them. Also, introduce the homomorphism from fuzzy AT-subalgebras and fuzzy AT-ideals are investigated. [ABSTRACT FROM AUTHOR]

The notion of an m-polar (∈ , ∈) -fuzzy a-ideal is introduced, and its properties are investigated. The relationship between m-polar fuzzy subalgebra, m-polar fuzzy ideal, and m-polar (∈ , ∈) -fuzzy a-ideal is examined. Conditions for an m-polar fuzzy ideal to be an m-polar (∈ , ∈) -fuzzy a-ideal are provided. The relationship between m-polar (∈ , ∈) -fuzzy p-ideal, m-polar (∈ , ∈) -fuzzy q-ideal, and m-polar (∈ , ∈) -fuzzy a-ideal is shown. The normal m-polar (∈ , ∈) -fuzzy a-ideal is introduced, and its characterizations are considered. Characterizations and extension property of an m-polar (∈ , ∈) -fuzzy a-ideal are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of state maps from a semihoop H1 to another semihoop H2, which is a generalization of internal states (or state operators) on a semihoop H. Also we give a type of special state maps from a semihoop H1 to H1, which is called internal state maps (or IS-maps). Then we give some examples and basic properties of (internal) state maps on semihoops. Moreover, we discuss the relations between state maps and internal states on other algebras. Then we introduce several kinds of filters by state maps on semihoops, called SM-filters, state filters and dual state filters, respectively, and discuss the relations among them. Furthermore we introduce and study the notion of prime SM-filters on semihoops. Finally, using SM-filter, we characterize two kinds of state semihoops.

The theory of fuzzy filters in pseudo-BE algebras is developed. Various characterizations of fuzzy filters are given. It is proved that the set of all fuzzy filters of a pseudo-BE algebra is a complete lattice. Some characterizations of Noetherian pseudo-BE algebras by fuzzy filters are obtained. Finally, fuzzy commutative filters are defined and studied. Moreover, the homomorphic properties of fuzzy (commutative) filters are provided. [ABSTRACT FROM AUTHOR]

In this paper, the notion of a η-Smarandache pseudo fuzzy ideal of a pseudo BH- algebra is introduced. Some propositions and examples are investigated to study properties of this notion and to determine the relationships between it and a η-Smarandache pseudo ideal of a pseudo BH-algebra [ABSTRACT FROM AUTHOR]

The notions of (∈ , ∈ ∨ q) -cubic p- (a- and q-) ideals of BCI-algebras are introduced and some related properties are investigated. Several characterization for these generalized (∈ , ∈ ∨ q) -cubic ideals are defined and relationship between (∈ , ∈ ∨ q) -cubic p-ideals, (∈ , ∈ ∨ q) -cubic q-deals and (∈ , ∈ ∨ q) -cubic a-ideals of BCI-algebras are discussed. [ABSTRACT FROM AUTHOR]

Lattice implication algebra is a new logical algebraic system which is established by combining lattice and implication algebra. As a generalization of intuitionistic fuzzy set, neutrosophic set is introduced which deals with indeterminate membership in addition to degree of membership and degree of non-membership. In this article, the notion of neutrosophic set theory is applied to lattice implication algebras. The concept of implicative neutrosophic LI-ideals of a lattice implication algebra is introduced, and several properties are investigated. Relationship between a neutrosophic LI-ideal and an implicative neutrosophic LI-ideal is discussed, and conditions for a neutrosophic LI-ideal to be an implicative neutrosophic LI-ideal are provided. Characterizations of an implicative neutrosophic LI-ideal are considered, and the extension property of an implicative neutrosophic LI-ideal is studied. [ABSTRACT FROM AUTHOR]

Fuzzy and multi set theories are recent approaches for information system and data mining. In this paper, we aim to construct correlation measure connected to these theories. We define fuzzy multi correlation measure and many of its properties are investigated, and some examples and applications are given. Also, we present new view of reduction for fuzzy multi information system. [ABSTRACT FROM AUTHOR]

We define direct product of (∈,∈ Vqk)-intuitionistic fuzzy sets and direct product of (∈,∈ Vqk)-intuitionistic fuzzy soft sets of subtraction algebras and investigate some related properties. [ABSTRACT FROM AUTHOR]

Characterizations of a (⋶, ⋶ ∨ q̄)-fuzzy subalgebra (ideal) are considered. Given an ∈-soft set, an (⋶, ⋶ ∨ q̄)-fuzzy subalgebra is established. Using the notion of (t, s)-fuzzy subalgebras, characterizations for an∈-soft set to be a (idealistic) soft BCK/BCI-algebra are provided. Using the notion of fuzzy p-ideals, a characterization of an∈-soft set to be a p-idealistic soft BCI-algebra is constructed. An equivalent condition for a q-soft set to be a p-ideal is given. Characterizations of a (∈,∈ ∨ q)-fuzzy p-ideal are initiated. Conditions for a (∈,∈∨ q)-fuzzy ideal to be a (∈,∈∨ q)-fuzzy p-ideal are stated. [ABSTRACT FROM AUTHOR]