Showing papers by "Bijan Davvaz published in 2014"

Attribute analysis of information systems based on elementary soft implications

Abstract: Soft set theory provides a parameterized treatment of uncertainty, which is closely related to soft computing models like fuzzy sets and rough sets. Based on soft sets and logical formulas over them, this study aims to present a new approach for revealing the causal relationship between values of attributes in an information system. The main procedure of our new method is as follows: First, we choose the attributes to be analyzed and construct some partition soft sets from a given information system. Then we compute the extended union of the obtained partition soft sets, which results in a covering soft set. Further, we transform the obtained covering soft set into a decision soft set and consider logical formulas over it. Next, we calculate various types of soft truth degrees of elementary soft implications. Finally, we can rank attribute values and plot some illustrative graphs, which helps us extract useful knowledge from the given information system. We use several examples, including a classical example given by Pawlak and a practical application concerning IT applying features analysis, to illustrate the newly proposed method and related concepts. In addition, we compare soft attribute analysis with rough attribute analysis and also relate it to soft association rules mining.

Structures of bipolar fuzzy Γ-hyperideals in Γ-semihypergroups

Abstract: The theory of bipolar fuzzy sets introduced by Lee [9] has been applied to many branches of mathematics. In this paper, we initiate a study on bipolar fuzzy sets in Γ-semihypergroups. We define bipolar fuzzy left (right, bi-, interior, (1,2)-) Γ-hyperideals and explore some related properties. We use these bipolar fuzzy Γ-hyperideals to characterize some classes of Γ-semihypergroups. We consider the Γ-semihypergroup $\underline{\mathcal{H}}$ of the bipolar fuzzy points of a Γ-semihypergroup H to discuss the relation between the bipolar fuzzy sub Γ-semihypergroup (left, right, bi-, interior, (1,2)-) Γ-hyperideal and the subsets of $\underline{\mathcal{H}}$ in a (regular) Γ-semihypergroup. In the end, we discuss in detail a number of results on homomorphic images and preimages of bipolar fuzzy Γ-hyperideals.

Topological Hypergroups in the Sense of Marty

Abstract: In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group. It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.

On fully regular \mathcal{AG }-groupoids

Abstract: One of the best approaches to study one type of algebraic structure is to connect it with other type of algebraic structure which is better explored. In this paper we have accomplished this aim by connecting \({\mathcal{AG }}\)-groupoids with some useful associative and commutative algebraic structures. We have also introduced a fully regular class of an \( {\mathcal{AG }}\)-groupoid and shown that an \({\mathcal{AG }}\)-groupoid \(\mathcal S \) with left identity is fully regular if and only if \(\mathcal{L=L }^{i+1}\), for any left ideal \(\mathcal L \) of \(\mathcal S \), where \(i=1,\ldots ,n\).

Degree Hypergroupoids Associated With Hypergraphs

Abstract: In this paper, we present some connections between graph theory and hyperstructure theory. In this regard, we construct a hypergroupoid by defining a hyperoperation on the set of degrees of vertices of a hypergraph and we call it a degree hypergroupoid. We will see that the constructed hypergroupoid is always an $H_v$-group. We will investigate some conditions on a degree hypergroupoid to have a hypergroup. Further, we study the degree hypergroupoid associated with Cartesian product of hypergraphs. Finally, the fundamental relation and complete part of a degree hypergroupoid is studied.

Hypergraphs and Hypergroups Based on a Special Relation

Abstract: The purpose of this paper is the study of hypergroups associated with hypergraphs. In this regards, we construct a ρ-hypergroup by means a given hypergraph by defining a special relation ρ, and then we investigate some related properties. Further, we introduce a special product of ρ-hypergroups. Also, we bridge between subhypergraphs and subhypergroups. Finally, the fundamental relation of a ρ-hypergroup is studied.

Fuzzy Γ-hypergroups

Abstract: In this paper, we introduce and analyze fuzzy Γ-hypergroups. We study fuzzy Γ-hypergroups and fuzzy Γ-hypergroup homomorphisms in connections with the associated Γ-hypergroups and Γ-hypergroup homomorphisms, respectively. Finally, since the fuzzy regular relations play an important role in getting quotient Γ-structures, we introduce and analyze fuzzy regular and fuzzy strongly regular relations on fuzzy Γ-hypergroups.

On modular inequalities of interval-valued fuzzy soft sets characterized by soft J-inclusions

Abstract: This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations of interval-valued fuzzy soft sets, we first investigate some basic properties of soft J-inclusions and soft L-inclusions. Then a new concept called upward directed interval-valued fuzzy soft sets is defined and some equivalent characterizations are presented. Furthermore, we consider modular laws in lattice theory and find that classical modular inequalities in lattice theory are not valid for interval-valued fuzzy soft sets. Finally, we present some interesting inequalities of interval-valued fuzzy soft sets by virtue of soft J-inclusions and related notions.

On Hyperideal Structure of Ternary Semihypergroups

Abstract: In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyperfilter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyperfilters in ternary semihypergroups. Some relationships between hyperfilters, prime hyper- ideals and hypersemilattice congruences in ternary semihypergroups are considered. We also introduce the notion of hyperideals extensions in ternary semihypergroups and some properties of them are investigated.

On Atanassov's intuitionistic fuzzy grade of the direct product of two hypergroupoids

Abstract: In this paper we continue the study of the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with the direct product of two hypergroupoids with special properties and we determine the Atanassov's intuitionistic fuzzy grade of such a sequence.

A note on fuzzy ordered $\mathcal{AG}$-groupoids

Abstract: Motivated by studying the structural properties of left right regular and intra-regular classes of an ordered semigroup, in this paper we have considered these classes in an ordered $\mathcal{AG}$-groupoid and shown that they coincide in a structure of an ordered $\mathcal{AG}$-groupoid with left identity. We have provided some useful connections between ordered $\mathcal{AG}$-groupoids and ordered semigroups. We have proved that every fuzzy right ideal of an ordered $\mathcal{AG}$-groupoid with left identity becomes a fuzzy left ideal but the converse is not valid. Moreover it has shown that a fuzzy left ideal and a fuzzy right ideal coincide in a left regular ordered $\mathcal{AG}$-groupoid with left identity. As an application of our results we get characterizations of left regular ordered $\mathcal{AG}$-groupoids in terms of fuzzy sets.

An introduction to the theory of algebraic multi-hyperring spaces

Abstract: A Smarandache multi-space is a union of n dierent spaces equipped with some dierent structures for an integer n 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of multi-hyperring theory. Some characterizations and properties of multihyperring spaces are investigated and obtained. Some open problems are suggested for further study and investigation.

Describing the Algebraic Hyperstructure of All Elements in Radiolytic Processes in Cement Medium

Abstract: Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of hyperstructures are the ones called Hv-structures. In the present paper, the algebraic hyperstructures (Hvstructures) are described for the elements in radiolytic processes in cement medium. These elements include e −, H2, OH − , H, O − , OH, H2O, HO − , H2O2, O − , O 2− 2 , HO2, O2, O − , O3 and O 2− which were reported by Bouniol and Bjergbakke, within a comprehensive model for describing radiolytic processes in cement medium.

Differential multiplicative hyperrings

Abstract: In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is in- troduced and some related properties are investigated.

An Investigation on Algebraic Structure of Soft Sets and Soft Filters over Residuated Lattices

Abstract: We introduce the notion of soft filters in residuated lattices and investigate their basic properties. We investigate relations between soft residuated lattices and soft filter residuated lattices. The restricted and extended intersection (union), and -intersection, cartesian product, and restricted and extended difference of the family of soft filters residuated lattices are established. Also, we consider the set of all soft sets over a universe set and the set of parameters with respect to , (), and we study its structure.

On Generalized Derivations of BCI-Algebras and Their Properties

Abstract: We introduce the concept of -derivations of BCI-algebras and we investigate some fundamental properties and establish some results on -derivations. Also, we treat to generalization of right derivation and left derivation of BCI-algebras and consider some related properties.

Atanassov's intuitionistic fuzzy grade of a class of non-complete 1-hypergroups

Abstract: This paper continues the study of the length of the sequence of join spaces and Atanassov's intuitionistic fuzzy sets associated with a hypergroup H. The classes of non-complete 1-hypergroups are considered and analyzed their Atanassov's intuitionistic fuzzy grade.

Join spaces, soft join spaces and lattices

Abstract: The aim of this paper is to initiate and investigate new (soft) hyperstructures, particularly (soft) join spaces, using important classes of lattices: modular and distributive. They are used in order to study (soft) hyperstructures constructed on the set of all convex sublattices of a lattice.

Ternary hypergroups (a survey)

Abstract: In this survey we study ternary semihypergroups and hypergroups and their connections with binary relations. In order to analyze quotient struc- tures, several kinds of equivalences are studied: regular, strongly regular; an important role in this study is dedicated to beta relation and we establish when it is transitive in a ternary semihypergroup. At the end of this survey, sev- eral kinds of ternary subhypergroups are introduced: conjugable, ultraclosed, invertible, closed, complete parts and the relationships among them are stud- ied. The heart of a hypergroup is extended to the heart notion in a ternary hypergroup.

n-ARY Hv-MODULES WITH EXTERNAL n-ARY P-HYPEROPERATION

Abstract: The class of (m;n)-ary Hv-modules is larger than the well known class Hv-modules. A wide subclass of (m;n)-ary Hv-modules is n-ary P-Hv-modules. In this paper, we consider and study a module over a ring and we dene three kinds of external n-ary P-hyperoperations. By using external n-ary P-hyperoperations and certain conditions, we construct several (m;n)-ary Hv-modules.

Fn-Hypergroups based on fuzzy hyperoperations and fundamental relations

Abstract: In this paper, the notion of fuzzy n-hypergroups Fn-hypergroups by using the notion of Fn-hyperoperations is introduced and some related properties are investigated. In this regards relationships between Fn-hypergroups and n-hypergroups are considered. Next, some properties of direct product of Fn-hypergroups are presented. We then study the quotient of Fn-hypergroups by a fundamental relation and describe some of their properties.

Intuitionistic Fuzzy Hyperideal Extensions of Semihypergroups

Abstract: The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, using Atanassov idea, we introduce the concepts of intuitionistic fuzzy hyperideal extension of semihypergroups and intuitionistic fuzzy prime (semiprime) hyperideal of semihypergroup. We discuss the properties of them and study the relationship between prime (semiprime) hyperideals and intuitionistic fuzzy prime (semiprime) hyperideals by means of the extensions of intuitionistic fuzzy hyperideals of semihypergroup.

An Introduction to the Theory of Algebraic Multi-Hyperring Spaces

Abstract: A Smarandache multi-space is a union of n dierent spaces equipped with some dierent structures for an integer n 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of multi-hyperring theory. Some characterizations and properties of multihyperring spaces are investigated and obtained. Some open problems are suggested for further study and investigation.

Introduction to Neutrosophic Nearrings

Abstract: The objective of this paper is to introduce the concept of neutrosophic near-rings. The concept of neutrosophic N-group of a neutrosophic nearring is introduced. We studied neutrosophic subnearrings of neutrosophic nearrings and also neutrosophic N-subgroups of neutrosophic N- groups.

Total Domination Subdivision Number in Strong Product Graph

Abstract: A set D of vertices in a graph G(V,E) is called a total dominating set if every vertex v∈V is adjacent to an element of D. The domination subdivision number of a graph G is the minimum number of edges that must be subdivided in order to increase the domination number of a graph. In this paper, we determine the total domination number for strong product graph and establish bounds on the total domination subdivision number for strong product graph.

KRASNER F (m;n) -HYPERRINGS

Abstract: $!!!!$ In this paper, the notion of fuzzy $!$ Krasner $!(m, n)$-hyperrings($!F^{(m, n)}!$-hyperrings) by using the notion of$F^m$-hyperoperations and $F^n$-operations is introduced and somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperring is extended by a Krasner $F^{(2,n)}$-hyperring. The concepts of normal $F$-hyperideals andhomomorphisms of Krasner $F^{(m, n)}$-hyperrings are adopted.Also, the quotient of Krasner $F^{(m, n)}$-hyperrings by definingregular relations are studied. Finally, the classical isomorphismtheorems of groups are generalized to Krasner $F^{(m,n)}$-hyperrings provided the $F$-hyperideals considered in themare normal.

A note on New fundamental relation of hyperrings

Abstract: In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. Commutative fundamental rings and the fundamental relation @a^* which is the smallest strongly regular relation in hyperrings were introduced by Davvaz and Vougiouklis (2007). Recently, another strongly regular relation named @q^* on hyperrings has been studied by Ameri and Norouzi (2013). Ameri and Norouzi proved that @q^* is the smallest strongly regular relation such that R/@q^* is a commutative ring. In this paper, we show that @q^* @a^* and @q^* is not the smallest strongly regular relation. Moreover, we show that some results of Ameri and Norouzi do not hold.