On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the intuitionistic fuzzification of the concept of sub-hyperquasigroups in a hyperquasigroup and investigate some properties of such sub-hyperquasigroups. In particular, we investigate some natural equivalence relations on the set of all intuitionistic fuzzy sub-hyperquasigroups of a hyperquasigroup.Comment: 13 page

Commutative Energetic Subsets of BCK-Algebras

The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal

Ordered semigroups characterized by (ϵ ϵ vqk)-fuzzy generalized bi-ideals

In this paper, we introduce a considerable machinery that permits us to characterize a number of special (fuzzy) subsets in ordered semigroups. In this regard, we generalize (Davvaz and Khan in Inform Sci 181:1759-1770 2011) and define (is an element of, is an element of boolean (ϵ ϵ vqk)-fuzzy generalized bi-ideals in ordered semigroups, which is a generalization of the concept of an (alpha, beta)-fuzzy generalized bi-ideal in an ordered semi-group. We also define (is an element of, is an element of boolean (ϵ ϵ vqk)-fuzzy left (resp. right)ideals. Using these concept, some characterization theorems of regular, left (resp. right) regular, completely regular and weakly regular ordered semigroups are provided. The upper/lower parts of an (is an element of, is an element of boolean (ϵ ϵ vqk)-fuzzy generalized bi-ideal and (is an element of, is an element of boolean (ϵ ϵ vqk)-fuzzy left (resp. right)-ideal are given, and some characterizations are provided

Characterizations of fuzzy fated filters of R0-algebras based on fuzzy points

More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of R0-algebras is discussed. The notion of an (∈,∈∨ qk)-fuzzy fated filter in a R0-algebra is introduced, and several properties are investigated. Characterizations of an (∈, ∈ ∨ qk)-fuzzy fated filter in an R0-algebra are discussed. Using a collection of fated filters, a (∈,∈∨ qk)-fuzzy fated filter is established

Neutrosophic N -Structures Applied to BCK/BCI-Algebras

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided

Ultra LILI-ideals in lattice implication algebras

summary:We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal

Ideal Theory in BCK/BCI-algebras in the Frame Of Hesitant Fuzzy Set Theory

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov’s intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra’s hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed