Search

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, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈ ∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α, β)-fuzzy subalgebras and (α, β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset. [ABSTRACT FROM AUTHOR]

Using the notion of the Łukasiewicz fuzzy set, we study the filter theory of Sheffer stroke Hilbert algebras. Here's what we're trying to do. 1. We first introduce the Łukasiewicz fuzzy filter of Sheffer stroke Hilbert algebras. 2. We provide an example to illustrates the Łukasiewicz fuzzy filter. 3. We examine the various properties of the Łukasiewicz fuzzy filter. 4. We discuss characterizations of the Łukasiewicz fuzzy filter. 5. We explore the conditions under which Łukasiewicz fuzzy set can be Łukasiewicz fuzzy filter. 6. We discuss the relationship between fuzzy filter and Łukasiewicz fuzzy filter. 7. We use the given filter to creates a Łukasiewicz fuzzy filter. 8. We present conditions for the three subsets, called ∈-set, q-set and O-set, to be filters. [ABSTRACT FROM AUTHOR]

Chen et al. [On coupon coloring of graphs, Discrete Appl. Math. 193 (2015) 94–101] had introduced the concept of coupon coloring for any graph with no isolated vertex. A k -coupon coloring of G is an assignment of colors from [ k ] : = { 1 , 2 , ... , k } to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [ k ]. The maximum k for which a k -coupon coloring exists is called the coupon coloring number of G , and is denoted by χ c (G). In this paper, we determine the coupon coloring number of Kneser graphs K (n , 2). [ABSTRACT FROM AUTHOR]

In this paper, considering L-algebras, which include a significant number of other algebraic structures, we present a definition of modules on L-algebras (Lmodules). Then we provide some examples and obtain some results on L-modules. Also, we present definitions of prime ideals of L-algebras and L-submodules (prime L-submodules) of L-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime L-submodules. [ABSTRACT FROM AUTHOR]

The aim of this paper is defining the concepts of Noetherian and Artinian hoops by using the filter of hoop in the partial order set of all the filters of hoops and inclusion relation and find some equivalent definitions for this notion. We translate some important results from theory of rings to the case of hoop and their characterizations are established. The relation between short exact sequence on Noetherian and Artinian hoop studied and by using short exact sequence we prove that the Cartesian product of two hoops is Noetherian (Artinian) if and only if each one is a Noetherian (Artinian). By using the notion of filter in hoops, we define the notion of composition series and prove any V-hoop is Noetherian and Artinian if and only if it has composition series. Finally, Chinese Remainder theorem in hoop and the relation between maximal filter and Noetherian (Artinian) hoop are investigated. [ABSTRACT FROM AUTHOR]

The k-deck of a graph is the multiset of its subgraphs induced by k vertices which is denoted by Dk(G). A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. Manvel proved that from the (n−l)-deck of a graph and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−1, the degree list of the graph is determined. In this paper, we extend this result and prove that if G is a graph with n vertices, then from the (n−l)-deck of G and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−3, where l ≥ 4 and n ≥ l + 6, the degree list of the graph is determined. [ABSTRACT FROM AUTHOR]

In this paper, we define the concepts of Engel, nilpotent and solvable BCI-algebras and investigate some of their properties. Specially, we prove that any BCK-algebra is a 2-Engel. Then we define the center of a BCI-algebra and prove that in a nilpotent BCI-algebra X, each minimal closed ideal of X is contained in the center of X. In addition, with some conditions, we show that every finite BCI-algebra is solvable. Finally, we investigate the relations among Engel, nilpotent and solvable BCI(BCK)-algebras.

The notion of a (limited) commutative T&F-ideal in BCK-algebras and BCIalgebras is introduced, and their properties are investigated. A relationship between a T&Fideal and a commutative T&F-ideal in BCK-algebras and BCI-algebras is established, and examples to show that any T&F-ideal may not be commutative are given. Proper conditions for a T&F-ideal to be commutative are provided. Using a commutative ideal of a BCKalgebra and a BCI-algebra, a commutative T&F-ideal is established. The closed T&F-ideal in a BCI-algebra is introduced, and a condition for a closed T&F-ideal to be commutative is discussed. Characterization of a commutative T&F-ideal in a BCI-algebra is considered. [ABSTRACT FROM AUTHOR]

In this paper, we apply the notion of n-fold filters to the EQ-algebras and introduce the concepts of n-fold pseudo implicative, n-fold implicative, n-fold obstinate, n-fold fantastic prefilters and filters on an EQ-algebra ε. Then we investigate some properties and relations among them. We prove that the quotient algebra ε/F modulo an 1-fold pseudo implicative filter of an EQ-algebra ε is a good EQ-algebra and the quotient algebra E/F modulo an 1-fold fantastic filter of a good EQ-algebra E is an IEQ-algebra. [ABSTRACT FROM AUTHOR]

The notion of (right) left mapping on equality algebras is introduced, and related properties are investigated. In order for the kernel of (right) left mapping to be filter, we investigate what conditions are required. Relations between left mapping and →-endomorphism are investigated. Using left mapping and →-endomorphism, a characterization of positive implicative equality algebra is established. By using the notion of left mapping, we define →-endomorphism and prove that the set of all →-endomorphisms on equality algebra is a commutative semigroup with zero element. Also, we show that the set of all right mappings on positive implicative equality algebra makes a dual BCK-algebra. [ABSTRACT FROM AUTHOR]

Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, "A" in relation to its opposite, "Anti-A" and that which is not A, "Non-A", and that which is neither "A" nor "Anti-A", denoted by "Neut-A". Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. In this article, we apply the notion of neutrosophic set theory to (positive implicative) ideals in BCK-algebras by using the concept of falling shadows. The notions of a positive implicative (∈, ∈)-neutrosophic ideal and a positive implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a positive implicative (∈, ∈)-neutrosophic ideal are considered, and relations between a positive implicative (∈, ∈)-neutrosophic ideal and an (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be a positive implicative (∈, ∈)-neutrosophic ideal are provided, and relations between a positive implicative (∈, ∈)-neutrosophic ideal, a falling neutrosophic ideal and a positive implicative falling neutrosophic ideal are studied. Conditions for a falling neutrosophic ideal to be positive implicative are provided. [ABSTRACT FROM AUTHOR]

In this paper, first we define the notion of an Engel polygroup, to get further properties on Engel fuzzy subpolygroups. Moreover, we prove that every normal fuzzy subpolygroup of an Engel polygroup is Engel. Furthermore, we introduce the notions of solvable and nilpotent fuzzy subpolygroups and we get some of their properties. Finally we investigate the relations among solvable and nilpotent fuzzy subpolygroups with Engel fuzzy subpolygroups. [ABSTRACT FROM AUTHOR]