# A. GhareebSouth Valley University · Department of Mathematics

A. Ghareeb

Professor

## About

87

Publications

9,983

Reads

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541

Citations

Citations since 2016

Introduction

A. Ghareeb received B.S. degree in mathematics from South Valley University in 2001 and, M.S. and Ph.D. degrees in topology from South Valley University in 2007 and 2009, respectively. He is currently Professor in Mathematics Department, Faculty of Science, South Valley University, Egypt. His current research interests include general topology, fuzzy topology, fuzzy mathematics, soft sets theory, algebra, and fuzzy algebra, similarity measures, and computer vision.

Additional affiliations

October 2017 - present

March 2014 - present

**Faculty of Science, South Valley University**

Position

- Professor (Associate)

October 2012 - present

**College of Science in Az Zulfi, Majmaah University**

Position

- Professor (Assistant)

Education

January 2007 - September 2009

**Faculty of Science, South Valley University**

Field of study

- Pure Mathematics-Topology

January 2005 - June 2007

**Faculty of Science, South Valley University**

Field of study

- Pure Mathematics-Topology

September 1997 - June 2001

**Faculty of Science, South Valley University**

Field of study

- Mathematics

## Publications

Publications (87)

In this paper, we introduce and study the concept of almost continuity in weak structures (Császár in Acta Math Hung 131(1--2):193--195, 2011) and discuss some of its characteristic properties. Finally, we give some applications of this new kind of continuity.

This paper takes some investigations on soft weak structures which are a generalization of weak structures and soft topological spaces with some separation axioms and compactness. Also, we give a systematic discussion on the relationship among these notions.

In this paper, a framework to hide privacy in video is proposed based on data hiding principals. A novel data hiding technique is proposed and implemented to hide the original frame into the in-painted one. The proposed hiding technique is carried out in the discrete wavelet transform domain of the cover video. The proposed technique is embedding v...

We present a new type of mappings called centrally extended α -homoderivations of a ring ℜ (i.e., a map H from ℜ into ℜ which satisfies H x + y − H x − H y ∈ Z ℜ and H x y − H x H y − H x α y − α x H y ∈ Z ℜ for any x , y ∈ ℜ ) where α is a mapping of ℜ and discuss the relationship between these mappings and other related mappings. Also, we study t...

The generalized growth of entire transcendental functions in terms of polynomial approximation errors in some Banach spaces has been studied by various authors. The main purpose of this paper is to study the harmonic polynomial approximation of entire harmonic functions in space ℝ n , n ≥ 3 , in certain Banach spaces. Moreover, the generalized type...

Based on the concept of pseudocomplement, we introduce a new representation of preopenness of L -fuzzy sets in R L -fuzzy bitopological spaces. The concepts of pairwise R L -fuzzy precontinuous and pairwise R L -fuzzy preirresolute functions are extended and discussed based on the i , j - R L -preopen gradation. Further, we follow up with a study o...

In this paper, we propose a novel model for 3D object watermarking. The proposed method is based on the properties of the discrete cosine transform (DCT) of the 3D object vertices to embed a secret grayscale image three times. The watermarking process takes place by using the vertices coefficients and the encrypted image pixels. Moreover, the extra...

Watermarking techniques in a wide range of digital media was utilized as a host cover to hide or embed a piece of information message in such a way that it is invisible to a human observer. This study aims to develop an enhanced rapid and blind method for producing a watermarked 3D object using QR code images with high imperceptibility and transpar...

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-...

Data hiding technique using steganography prospered widely due to its high un-detectability, flexibility to the size of hidden data, and robustness against compression and other image processes. Accordingly, this paper aims to use a steganographic technique based on DICOM medical images, where one medical image is used as a cover image, and the oth...

Based on the concepts of pseudocomplement of L-subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL-fuzzy compactness degree and the Lindelöf property degree of an L-subset in RL-fuzzy topology are introduced and characterized. Since L-fuzzy topology in the...

In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, the degree of L,M-fuzzy concavity is introduced and characterized as a generalization of L-concave structure and L,M-fuzzy concave structure. Based on that, the degree of L,M-fuzzy concavity preserving and L,M-fuzzy concave-to-concave of...

Watermarking provides an efficient mechanism for copyright protection of digital media by embedding information in the object to identify the owner. This paper proposed a watermarking technique that can successfully embed a grey-scale image in a 3D mesh object. In our proposed technique, each three vertices of the 3D object can hide one pixel from...

The aim of this paper is mainly to study the (L, M)-fuzzy measurability in view of degree. Firstly, we generalize the notion of (L, M)-fuzzy σ-algebra by defining the degree of an (L, M)-fuzzy σ-algebra with respect to a mapping σ : L X ⟶ M. Such kind of degrees is proved to satisfy some axioms of (L, M)-fuzzy σ-algebra. Additionally, we define and...

Sensors are the modules or electronic devices that are used to measure and get environmental events and send the captured data to other devices, usually computer processors allocated on the cloud. One of the most recent challenges is to protect and save the privacy issues of those sensors data on the cloud sharing. In this paper, sensors data colle...

In this paper, we present a new vision for studying F-open, F-continuous, and F-irresolute function in (L,M)-fuzzy topological spaces based on the implication operation and (L,M)-fuzzy F-open operator [3]. These kinds of functions are generalized with their elementary properties to (L,M)-fuzzy topological spaces setting based on graded concepts. Mo...

This paper presents a new representation of α -openness, α -continuity, α -irresoluteness, and α -compactness based on L -fuzzy α -open operators introduced by Nannan and Ruiying [1] and implication operation. The proposed representation extends the properties of α -openness, α -continuity, α -irresoluteness, and α -compactness to the setting of L...

The aim of this paper is to present the degree of semi-preopenness, semi-precontinuity, and semi-preirresoluteness for functions in (L, M)-fuzzy pretopology with the help of implication operation and (L, M)-fuzzy semi-preopen operator introduced by [Ghareeb A., L-fuzzy semi-preopen operator in L-fuzzy topological spaces, Neural Comput. & Appl., 201...

In this paper, we will introduce the notions of semiopenness, semicontinuity, preopenness, precontinuity, irresolutness and preirresolutness degree of functions in (L, M)-fuzzy topological spaces based on the implication operation. Their elementary properties in topology will be extended to the setting of (L, M)-fuzzy topology through graded concep...

It has been noticed that among the different fields of theoretical mathematics where soft sets theory is applied extensively, the most of papers are related to topology. In this paper, the concept of soft weak baire spaces, i.e., the soft generalization of the concept of weak baire spaces as defined by Renukadevi and Muthulakshmi [1] has been prese...

The concept of coupled semi-quantales is introduced. An adjunction between the category of coupled semi-quantales and the category of lattice-valued biquasi-topological spaces is established. The topological and the lattice-theoretic concepts of regularity and compactness are extended to both lattice-valued biquasi-topological spaces and coupled se...

Measuring the distance or similarity objectively between images is an essential and a challenging problem in various image processing and pattern recognition applications. As it is very difficult to find a certain measure that can be successfully applied to all kinds of images comparisons-related problems in the same time, it is appropriate to look...

In this paper we introduce the concepts of (r, s)-generalized fuzzy semi-extremally disconnectedness spaces and study effect of generalized double fuzzy semi-irresolute and generalized double fuzzy semiopen functions in this space. Moreover, we investigate some interesting relationship between generalized double fuzzy semiopen functions and (r, s)-...

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^\star(U),\sqsubseteq)$ and $(Ds(\varphi(U)),\subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

The concept of a coupled quantales is introduced as a non-commutative extension of the concept of biframes. Also an approach to non-commutative bitopology is studied. Then an adjunction between the category of coupled quantales and the category of biquantum spaces is established.

The present article discuss (alpha,beta)-generalised fuzzy pre border, (alpha,beta)-generalised fuzzy pre-exterior and (alpha,beta)-generalised fuzzy pre-frontier in double fuzzy topologies. Furthermore, some characterisations of generalised double fuzzy pre-continuous, generalised double fuzzy preopen, generalised double fuzzy preclosed and genera...

The present article discuss (α, β) -generalised fuzzy pre-border (α, β) - generalised fuzzy pre-exterior and (α, β) -generalised fuzzy pre-frontier in double fuzzy topologies. Furthermore, some characterisations of generalised double fuzzy pre-continuous, generalised double fuzzy preopen, generalised double fuzzy preclosed and generalised double fu...

The purpose of this paper is to introduce the concept of soft double fuzzy semi-topogenous order. Firstly, we give the deﬁnition of soft double fuzzy semi-topogenous order. Secondly, we induce a soft double fuzzy topology from a given soft double fuzzy semi-topogenous order by using soft double fuzzy interior operator.

The notions of SP-compactness degree, SP-separatedness degree and SP-connectedness degree of an L-subset are discussed in L-fuzzy pretopological spaces via L-fuzzy semi-preopen operator and implication operator. The new notions do not based on the basis lattice structure, so the distributivity can be neglected. The notions SP-compactness, SP-separa...

This comment refers to the original article with article doi:10.1007/s40096-014-0124-7 (Math Sci (2014) 8:124).

The purpose of this paper is to introduce and study a new class of sets called (r, s)-generalized fuzzy b-regular
weakly closed sets which is lies between the new class of (r,s)-fuzzy regular weakly closed sets and (r,s)-generalized fuzzy
b-closed sets in double fuzzy topological spaces. Several fundamental properties are introduced and discussed....

The purpose of this paper is to introduce the notions of several types of semi-compactness in double fuzzy topological spaces known as generalized double fuzzy semi-compactness, generalized double fuzzy nearly semi-compactness and generalized double fuzzy weakly semi-compactness. Some interesting properties and characterizations of the new concepts...

We correct some mistakes in the paper: “On soft preopen sets and soft pre separation axioms”, Gazi University Journal of Science, 27(4)(2014), 1077-1083.

In this paper, we introduce and study the properties of some new kinds of generalized closed subsets with respect to a weak structure modified by a hereditary class. Then some already established results are generalized. Also, we define a new kind of continuity depending on the new class of generalized closed subsets.

The purpose of this paper is to introduce and study a new class of fuzzy sets called (r, s)-generalized fuzzy b-closed sets and (r, s)-generalized ⋆-fuzzy b-closed sets in double fuzzy topological spaces. Furthermore, the relationships between the new concepts are introduced and established with some interesting examples.

In this paper, we introduce a new class of functions called L-double fuzzy weakly semi-preopen (semi-preclosed) functions in L-double fuzzy topological spaces. Some characterizations of this class and its properties and the relationship with other classes in L-double fuzzy topological spaces are also discussed.

This paper gives fundamental concepts and properties of a soft spatial region. We provide a theoretical framework
for both dominant ontologies used in GIS.

This article has no abstract.

This paper makes some investigations on weak structures with some (w)-
separation axioms. Also, we give a systematic discussion on the relationship among these
notions. Moreover, we present the product of such structures.

The aim of this paper is to define the concept of fuzzy k 0-preproximity and show how a fuzzy closure space is induced by a fuzzy k 0-preproximity and vice versa. Also, we introduce the notion of fuzzy k 0-preproximal neighborhood system.

In this paper, we introduce the concept of generalized double fuzzy semi-basically disconnected space and related notions such as (r, s)-generalized fuzzy semiopen-F σ sets, (r, s)-generalized fuzzy semiclosed-G δ sets, generalized double fuzzy semi *-open function, generalized double fuzzy semi *-continuous function and generalized double fuzzy se...

We introduce the notions of totally continuous functions, totally semicontinuous functions, and semitotally continuous functions in double fuzzy topological spaces. Their characterizations and the relationship with other already known kinds of functions are introduced and discussed.

The aim of this paper is to use the notion of Ψ-operations in double fuzzy topological spaces to study the concept of (r,s)-fuzzy generalized Ψρ-closed sets and (r,s)-fuzzy generalized Ψρ-open sets, some characterizations and properties of these concepts are given. Moreover, we discussed the relationship between these sets in double fuzzy topologic...

The aim of this paper is to introduce the concepts of somewhat slightly generalized double fuzzy semicontinuous functions and somewhat slightly generalized double fuzzy semiopen functions in double fuzzy topological spaces. Some interesting properties and characterizations of these functions are introduced and discussed. Furthermore, the relationsh...

In this paper, we introduce the concepts of slightly double fuzzy continuous functions and slightly generalized double fuzzy semicontinuous functions in double fuzzy topological spaces. Several interesting properties and characterizations are introduced and discussed. Furthermore, the relationships among the new concepts are introduced and establis...

In this paper, we introduce and characterize the concepts of generalized closed (gw-closed, for short) sets in weak structures which introduced by Csaszar [3] and we give some properties of these concepts. The concept of gw-closed sets (in the sense of Al Omari and Noiri [1]) is a special case of gw-closed sets presented here. Finally, the concepts...

In this paper, the concept of fuzzy \(Cs(\mathfrak {I})\) -closed spaces is introduced in fuzzy topological spaces. Several characterizations and some interesting properties of these spaces are discussed. Finally the image of \(Cs(\mathfrak {I})\) -closeness under some functions is introduced and characterized.

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 Gamma-semihypergroups. We define bipolar fuzzy left (right, bi-, interior, (1, 2)-) Gamma-hyperideals and explore some related properties. We use these bipolar fuzzy Gamma-hyperideals t...

The purpose of this paper is to introduce and characterize the concepts of ψ-operations in double fuzzy topological spaces. Also, we use them to study (r,s)-generalized fuzzy ψρ-closed sets and (r,s)-generalized fuzzy ψρ-open sets. Some characterizations and properties for these concepts are discussed.

In this paper, we introduce the concept of interval valued fuzzy LA-subsemigroups (left, right, two-sided, interior, bi-) ideals in LA-semigroups. Also we prove some results on direct product of interval valued fuzzy ideals in LA-semigroups.

In this paper, we used the concept of (L, M)-fuzzy remote neighborhood system to study and establish the convergence theory of molecular nets. Next, we introduce the Ti-axioms (i = −1, 0, 1, 2) in (L, M)-fuzzy topological molecular lattices, and discuss some of their characterizations. Finally, we show that the Ti-axioms (i = −1, 0, 1, 2) are prese...

In this paper, we introduce and study the concept of Λ-generalized closed sets with respect to an ideal bitopological space,
which are the extension of the concept of Λ-generalized closed sets in topological and bitopological spaces.

In this paper, we introduce and characterize double fuzzy weakly preopen and double fuzzy weakly preclosed functions between I-double gradation fuzzy topological spaces and also study these functions in relation to some other types of already known functions.

The left and right regular classes of a semigroup theory plays essential role in studying the structural properties of the associative algebraic structure. In this paper, we show that these two classes coincides in an
${\mathcal{AG}}$
-groupoid with left identity which is a non-associative algebraic structure. As an application of our results we...

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, continuity, proximity, uniformity, and syntopogenous structures. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in t...

In this paper, we show that the construction arising from a generalized topology and a hereditary class introduced by Á. Császár (2007) [9] remains valid, together with many applications, if the generalized topology is replaced by a weak structure.

In this paper, we show that the construction arising from a generalized topology and a hereditary class introduced by A. Csaszar (2007) [9] remains valid, together with many applications, if the generalized topology is replaced by a weak structure. Crown Copyright

A general framework for the concepts of compactness, countable compactness, and the Lindelöf property is introduced in L-topological spaces by means of several kinds of open L-sets and their inequalities when L is a complete DeMorgan algebra. The method used in this paper shows that these results are valid for any kind of open L-sets and thus we do...

The aim of this paper is to use the notion of (r, s)-fuzzy regular
semiopen sets to introduce Rs-compactness in double fuzzy topological
spaces. The notions of (r, s)-fuzzy Rs-compactness, (r, s)-fuzzy almost Rscompactness
and (r, s)-fuzzy weakly Rs-compactness have been studied,
some properties of these compactness are studied.

In this paper, we use an L-fuzzy semi-preopen operator introduced in Ghareeb (2011) to study the degree of semi-preseparatedness and the degree of semi-preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of semi-preconnectedness are presented in L-fuzzy topological spaces.

In this paper, we give the concept of LL-fuzzy FF-open operator in LL-fuzzy topological spaces, and use it to introduce a new form of FF-compactness in LL-fuzzy topological spaces. We also study some properties of LL-fuzzy FF-compactness.

In this paper, we introduce the notion of ΛΛ-generalized closed sets in bitopological spaces. Also, we give some characterizations and applications of it.

We introduce the concept of L-double uniform spaces in Hutton's sense. We prove the category of L-double uniform spaces is topological category over SET. The natural relationships between L-double uniformities, L-double fuzzy topologies and L-double fuzzy topogenous structures are studied. The family coproduct(eta, eta*) of all L-double uniformitie...

In this paper, we introduce and characterize several types of normality in double fuzzy topological spaces. The effects of some types of functions on these types of normality are introduced.

In this paper, we use L-fuzzy preopen operator to introduce the degree of pre-separatedness and the degree of preconnectedness in L-fuzzy topological spaces. Many characterizations of the degree of preconnectedness are presented in L-fuzzy topological spaces.

A new class of functions called L-fuzzy weakly Semi-Preopen (Semi-Preclosed) functions in L-fuzzy topological spaces are introduced in this paper. Some characterizations of this class and its properties and the relationship with other classes of functions between L-fuzzy topological spaces are also obtained.

In this paper, double fuzzy semi- topogenous structures was introduced and characterized. The relationships with double fuzzy topology, double fuzzy quasi-proximity are introduced.

In this paper, we introduce (r;s)-semi generalized fuzzy closed sets in double fuzzy topological spaces in Kubiak- ˇ Sostak sense and investigate some of their properties. More- over, we introduce and study the generalized forms of fuzzy irresolute functions between double fuzzy topological spaces. Copyright c ∞ 2010 Yang's Scientific Research Inst...

In this paper, we introduce the notion of rough IF-subgroup with respect to an IF-normal subgroup of a group, and give some properties of the lower and the upper approximations in a group.

We introduce the concepts of (r,s)-fuzzy F-open and (r,s)-fuzzy F-closed sets in double fuzzy topological spaces. We used them to explain the notions of (r,s)-fuzzy F-closed spaces. Also, we give some characterization of (r,s)-fuzzy F-closeness in terms of fuzzy filterbasis. Editorial remark: There are doubts about a proper peer-reviewing procedure...

In this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the initial structures of double fuzzy preproximity spaces. Furthermore, we have prove...

In this paper, we introduce and characterize fuzzy weakly preopen and fuzzy weakly preclosed functions between L-fuzzy topological spaces in Kubiak–Šostak sense and also study these functions in relation to some other types of already known functions.

In this paper, we introduce multi-intuitionistic fuzzy sets and intuitionistic fuzzy hybrid sets. The basic operations between such structures are defined. The use of these structures in the definition of intuition is tic fuzzy variants of P systems and their properties are presented.

We will prove the existence of flnal intuitionistic fuzzy topological spaces and flnal intuitionistic fuzzy closure spaces. From this fact, we can deflne intuitionistic quotient spaces of their spaces and sum of intuitionistic fuzzy closure spaces. In this paper, addi- tivity of two kinds of intuitionistic fuzzy closure spaces are studied.

We will prove the existence of final intuitionistic fuzzy topological spaces and final intuitionistic fuzzy closure spaces. From this fact, we can define intuitionistic quotient spaces of their spaces and sum of intuitionistic fuzzy closure spaces. In this paper, addi-tivity of two kinds of intuitionistic fuzzy closure spaces are studied.

We introduce and characterize r-Lc open, r-Lc semiopen sets (resp. r-Lc closed, r-Lc semicosed sets) and Lc-open, Lc-semiopen and Lc-semi maps (resp. Lc-closed, Lc-semiciosed maps) in L-fuzzy closed space.

In this paper, we introduce the concept of double fuzzy preproximity spaces as a generalization of a fuzzy preproximity spaces and investigate some of their properties. Also we study the relationships between double fuzzy preproximity spaces, double fuzzy topological spaces and double fuzzy closure spaces. In addition to this was the introduction o...

In this paper, we introduce the concepts of -fuzzy feebly open and -fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of -fuzzy F-closed spaces. Also, we give some characterization of -fuzzy F-closedness in terms of fuzzy filterbasis and -fuzzy feebly--cluster points.

The authors introduce and characterize r-open, r-semiopen sets (resp. r-closed, r-semiciosed sets) and open, semiopen and semicontinuous maps (resp. closed, semiclosed maps) in L-fuzzy closure spaces.

## Questions

Question (1)

I need a method to compute the homogeneity of a digital image in intuitionistic fuzzy sets theory? If there is a method for fuzzy sets theory that can be extended to the intuitionistic case, point out it for me..