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Let Bk be the nonbinary Boolean semiring and A be a m x n Boolean matrix over Bk. The Boolean rank of a Boolean matrix A is the smallest k such that A can be factored as an m x k Boolean matrix times a k x n Boolean matrix. The isolation number of A is the maximum number of nonzero entries in A such that no two are in any row or any column, and no two are in a 2 x 2 submatrix of all nonzero entries. We have that the isolation number of A is a lower bound on the Boolean rank of A. We also compare the isolation number with the binary Boolean rank of the support of A, and determine the equal cases of them. [ABSTRACT FROM AUTHOR]

Given i; j; k ∈ {1; 2; 3; 4}, the notion of (i; j; k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided. [ABSTRACT FROM AUTHOR]

In a wide spectrum of mathematical issues, the presence of a fixed point (FP) is equal to the presence of a appropriate map solution. Thus in several fields of math and science, the presence of a fixed point is important. Furthermore, an interesting field of mathematics has been the study of the existence and uniqueness of common fixed point (CFP) and coincidence points of mappings fulfilling the contractive conditions. Therefore, the existence of a FP is of significant importance in several fields of mathematics and science. Results of the FP, coincidence point (CP) contribute conditions under which maps have solutions. The aim of this paper is to explore these conditions (mappings) used to obtain the FP, CP and CFP of a neutrosophic soft set. We study some of these mappings (conditions) such as contraction map, L-lipschitz map, non-expansive map, compatible map, commuting map, weakly commuting map, increasing map, dominating map, dominated map of a neutrosophic soft set. Moreover we introduce some new points like a coincidence point, common fixed point and periodic point of neutrosophic soft mapping. We establish some basic results, particular examples on these mappings and points. In these results we show the link between FP and CP. Moreover we show the importance of mappings for obtaining the FP, CP and CFP of neutrosophic soft mapping. [ABSTRACT FROM AUTHOR]

In this paper, we have shown that a locally associative Γ-AG**-groupoid S has associative powers and S/ρΓ is a maximal separative homomorphic image of S, where aρΓb implies that aΓbΓn = bΓn+1, bΓaΓn = aΓn+1, ∀a, b ∈ S. The relation ηΓ is the least left zero semilattice congruence on S, where ηΓ is defined on S as aηΓb if and only if there exist some positive integers m; n such that bΓm ⊆ aΓS and aΓn ⊆ bΓS. [ABSTRACT FROM AUTHOR]

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (∈, ∈ V (k, qk))-fuzzy bi-ideals of an ordered semigroup S. Further, upper/lower parts of (∈, ∈ V (k, qk))-fuzzy bi-ideals of S are determined. Finally, some well-known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (∈, ∈ V (k, qk))-fuzzy bi-ideals. [ABSTRACT FROM AUTHOR]

For i,j,k,l,m,n ∊ {1,2,3,4}, the notion of (T(i, j),I(k, l),F(m, n))-interval neutrosophic ideals in BCK/BCI-algebras is introduced, and their properties and relations are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we consider an ordered LA-semihypergroup and discuss its roughness. In particular, we study some properties of rough hyperideals, rough bi-hyperideals and rough quasi-hyperideals in ordered LA-semihypergroups using the pseudohyperorder relations. Finally, we investigate the idea of direct product of sub LA-semihypergroups and prove some results in this regard. [ABSTRACT FROM AUTHOR]