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In this paper, we apply the theory of modules on hoops and introduce two concepts of modules on hoops and provide special examples and interesting results. Both concepts are correct and logical. The first concept is very close to the definition of module in abstract algebra. In this case, we investigate some important results in modules such as sub-modules and quotient structures. But if we want to investigate the relationship between hoop-modules and other modules on logical algebraic structures such as B C K -modules and M V -modules, we need to define the second definition of hoop-modules. In this case, we can get that a B C K -modules and an M V -module from any hoop-module. [ABSTRACT FROM AUTHOR]

EQ-algebras were introduced by Novák in [14] as an algebraic structure of truth values for fuzzy type theory (FFT). In [1], Borzooei et. al. introduced the notion of preideal in bounded EQ-algebras. In this paper, we introduce various kinds of preideals on bounded EQ-algebras such as Λ-prime, ⊗-prime, ∩-prime, ∩-irreducible, maximal and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded EQ-algebra, any proper preideal is included in a Λ-prime preideal. In the following, we show that the set of all Λ-prime preideals in a bounded EQ-algebra is a T0 space and under some conditions, it is compact, connected, and Hausdor. Moreover, we show that the set of all maximal preideals of a prelinear involutive bounded EQ-algebra is an Uryshon (Hausdor) space and for a finite EQ-algebra, it is T3 and T4 space. Finally, we introduce a contravariant functor from the categories of bounded EQ-algebras to the category of topological spaces.

In this paper, we introduced the concept of a soft hoop and we investigated some of their properties. Then, we established different types of intersections and unions of the family of soft hoops. We defined two operations ⊙ and → on the set of all soft hoops and we proved that with these operations, it is a hoop and also is a Heyting algebra. Finally we introduced a congruence relation on the set of all soft hoops and we investigated the quotient of it.

One of the most critical concepts in the study of groups is the notion of nilpotency. Nilpotent groups arise in Galois theory, as well as in the classification of groups. In this paper, we apply the notion of nilpotency on B C K -algebras by using fuzzy ideals. First we define the concept of nilpotent fuzzy ideal in B C K -algebras and investigate their properties. Furthermore, we find some relation between fuzzy nilpotent ideals and quotient B C K -algebras. Specially, we construct a nilpotent B C K -algebra by using a fuzzy nilpotent ideal. Finally, we prove that any minimal ideals of a B C K -algebra X , is contained in the center of any fuzzy nilpotent ideals of X. [ABSTRACT FROM AUTHOR]

In this paper the meanings of neutrosophic special n-dominating set, neutrosophic special n-domination number, inverse neutrosophic special domination set (number) and inverse neutrosophic special n-domination number are introduced and some of related results are investigated. Finally, an application of inverse neutrosophic special dominating set in decision making under ashy clauses between certainty and uncertainty is provided. In fact, we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences. [ABSTRACT FROM AUTHOR]

In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology. [ABSTRACT FROM AUTHOR]

Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.

The domatic number d(G) of a graph G is the maximum k for which V (G) can be partitioned into k pairwise disjoint dominating sets. In this paper, we determine the domatic numbers of complete graphs, complete k-partite graphs, Johnson graphs J(n, 2), unicyclic graphs, bicyclic graphs and generalized Θ-graphs. [ABSTRACT FROM AUTHOR]

In this paper, by considering the notion of fuzzy hyperoperation, we define the concept of fuzzy hyper B C K (B C I) -algebras as a generalization of B C K (B C I) -algebras and study related properties. Moreover, we introduce the notions of fuzzy hyper B C I -ideal and weak (strong) fuzzy hyper B C I -ideal, and then examine the relations among them. Finally, we investigate the relation between fuzzy hyper B C I -algebras with fuzzy hypersemigroup, fuzzy hypergroup and hyper B C I -algebras. [ABSTRACT FROM AUTHOR]

After introducing the concept of single valued neutrosophic ideal in a pseudo MV-algebra, its properties are examined. The various conditions under which a single valued neutrosophic set can be a single valued neutrosophic ideal are examined. Characterizations of a single valued neutrosophic ideal of a pseudo MV-algebra are considered. [ABSTRACT FROM AUTHOR]

In this paper, by considering the notion of upsets, for any element x of a BL-algebra L, we construct a topology Tx on L and show that L-algebras with this topology formes a semitopological BL-algebras. Then we obtain some of the topological aspects of this structure such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of MV -algebra and show that they are equivalent.

We study hoops in order to give some new characterizations for regular and Boolean elements in hoops and we study the relationship between them. Specially, we prove that any bounded v̲-hoop is a Stone algebra if and only if MV -center set and Boolean elements set are equal. Then we define the concept of regular filter in hoops and v̲-hoops with RF-property and peruse some properties of them. In addition, we show that each Y-hoop with RF-property, is a Boolean algebra and any hoop A with RF-property such that B(A) = {0, 1}, is a local hoop. Finally, we prove that any hoop A has RF-property if and only if Spec(A) = Max(A) and if and only if A is a hyperarchimedean. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new kinds of graphs based on equality algebras. First of all, by using the meet operation we define the notion of zero divisors on equality algebra and study related properties. Then we introduce a meet graph on equality algebra by using zero divisors. In addition, we investigate some conditions for a meet graph to be a complete, connected and a star graph. Also, by using the notion of filters in equality algebras, we define an equivalence relation on equality algebras and then by using the equivalence classes we introduce two kinds of graphs on them. Finally, conditions for a graph based on these classes to be connected, or bipartite, or complete, or planar or an outer-planar graph are provided. [ABSTRACT FROM AUTHOR]