International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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A research on the fifth case of the triangulation cases

Abdelmohaymen Mohammed Abdulaziz Fawaz

Mathematics teacher at Al-Azhar Al-Sharif

ABSTRACT

This research aims to conclude a fifth case of the cases of congruent triangles, the case of the equal triangles in the area. As we know, if the triangles are identical, then they are equal in space and vice versa is not always true. So this research is focused on the situation in which the equal triangles in the area are to be congruent and the required conditions, for them, to get matched. After the study mentioned in the research, and with the availability of some elements, I was able to get to the text of the fifth case of the cases of congruent triangles which states:
“The two equal triangles correspond to the area if a rib and an angle match in one of the triangles with their counterparts in the other triangle”

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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Attributes priority arrangement of cancellations in the life insurance using rough set

M. A. Elsafty , H. M. Elkhawaga , A.M.Kozae

Department of Mathematics and Statistics, Faculty of Science, Taif University

Department of Statistics and Mathematics and Insurance, Tanta University, Egypt

Department of Mathematics, Faculty of Science, Tanta University, Egypt

ABSTRACT

In this paper, we present a new method to rough set attributes priority arrangement of cancellations in the life insurance, the number of canceled documents on the rise plus they oscillatory also in rates of cancellations in constant fluctuation which requires searching in the problem of cancellations of these documents where, these cancellations affect negatively the results of the Egyptian life insurance operations of insurance companies. This paper also aims to identify the most important variables that affect the rates of cancellations and so as to reach solutions that lead to reducing the number of canceled documents by using the Rough Model. The research also aims to use the Rough model to identify the determinants of cancellations in the life insurance of the Egyptian insurance market, so as to reach solutions that lead to reducing the number of canceled policies and find solutions to them. Our findings proved that the most important factors that affect the document cancellation in the Egyptian life insurance policies are; policy premiums, insurance period and age of policyholders respectively.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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11

Results on generalized fuzzy soft topological spaces

F.H. Khedr , S.A. Abd El-Baki , M.S. Malfi

Assiut University

Assiut University

Assiut University

ABSTRACT

In this manuscript, the concept of a generalized fuzzy soft point is introduced and some of its basic properties are studied. Also, the concepts of a generalized fuzzy soft base (subbase) and a generalized fuzzy soft subspace are introduced and some important theorems are established. Finally, we study the relationship between fuzzy soft set, intuitionistic fuzzy soft set, generalized fuzzy soft set and generalized intuitionistic fuzzy soft set are investigated.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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11

Soft rough approximation operators via ideal with application in decision making

Heba Ibrahim Mustafa

Faculity of science Zagazig University

ABSTRACT

Theories of soft sets and rough sets are two different approaches to vagueness. They can be combined to form a powerful mathematical tool for dealing uncertain problems. Soft rough set introduced by Feng[7] is the connection between these approaches and it is the generalization of rough set with respect to the soft approximation space. This paper extend soft rough approximation model by defining new soft rough approximation operators via ideal. When the ideal is the least ideal of $\wp(U)$, these two approximations coincide. We present the essential properties of new opertors via ideal and supported by illustrative examples. The notion of soft rough equal relations via ideal is proposed and related examples are examined. We also show that rough set via ideal [26] can be viewed as a special case of soft rough set via ideal, and these two notions will coincide provided that the underlaying soft set is a partition soft set. We obtain the structure of soft rough set via ideal, gives the structure of topologies induced by soft set and an ideal. Moreover, an example containing a comparative analysis between rough sets via ideal and soft rough sets via ideal is given. We show that soft rough approximation via ideal could provide a better approximation than rough set via ideal. Finally application of data reduction are done and an algorithm of multi-attribute decision making based on soft rough sets via ideal is given.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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A multi-set function

Fawsia Sleim

Faculity of science Zagazig university

ABSTRACT

In this paper, we study the cartesian product of two multi-sets and some of its properties . Also we study the multi-set function and some of its properties and define the image and the inverse image of multi- sets and study of some properties .We study the multi-order relation ,multi-increasing ( decreasing ) function ,and the multi-topological ordered spaces and some of m - separation axioms of multi-topological spaces

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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On modified Soft rough sets on a complete atomic Boolean lattice

Heba

Zagazig University

ABSTRACT

Soft set theory and rough set theory are treated as mathematical approaches to deal with uncertainty. They are combined together by F.Feng et al. In[ ], we introduce the notion of soft rough sets on a complete atomic Boolean lattice as a generalization of soft rough sets. In this paper, we strengthen the concept of soft rough on a complete atomic Boolean lattice by defining the concept of MSR sets on a complete atomic Boolean lattice. In this model, some properties which were not satisfied in soft rough sets on a complete atomic Boolean lattice can be proved. Finally, the notion of lower and upper MSR-approximations of soft sets on a complete atomic Boolean lattice is studied.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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SMOOTH HESITANT FUZZY TOPOLOGICAL SPACES

Fawsia

Zagazig university

ABSTRACT

In this paper, we define the basic concepts of hesitant fuzzy sets and smooth hesitant fuzzy topologies in $\hat{S}$ostak sense. We study and investigate some properties of smooth hesitant fuzzy topological spaces. Moreover, we introduce the concepts of smooth hesitant closure and smooth hesitant interior of a fuzzy hesitant set and obtain some of their structural properties.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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On nano pre-I-open sets and a decomposition of nano I-continuity

Abd El Fattah A. El Atik , Arafa A. Nasef

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Department of Physics and Engineering Mathematics, Faculty of Engineering Kafrelsheikh University, Egypt.

ABSTRACT

In this paper, we introduce and study the notion of nano pre-I-open sets which is properly placed between nano openness and nano preopenness regardless the nano topological ideal. Also, we show that the class of near pre-I-open sets is properly places between the classes of nano I –open and nano preopen sets. We give a decomposition of nano I-continuity by proving that a function f(X,τ,I)→(Y,σ) is nano I-continuous if and only if it is nano I-continuous and nano *-I-continuous .

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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New Types of separation axioms on Graphs

Abd El Fattah A. El Atik , Mohammed atef

Department of mathematics, Faculty of Science, Tanta University.

Department of mathematics, Faculty of Science, Menoufia University.

ABSTRACT

The focus of this article is to define a new definition of the neighborhood which is built on the choice of the distance between two vertices. A comparison between these types of results from a new formed topologies and neighborhoods is discussed. Through the edges between vertices in any graph, we introduce a new class of separation axioms called graph separation axioms. Also, we study the connections between these graph separation axioms.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

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Magnetic curves of spherical images in Euclidean space

H. S. Abdel-Aziz , M. Khalifa Saad , Haytham. A. Ali

Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt.

Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt.

Mathematics Department, Faculty of Science, Sohag University, 82524, Egypt.

ABSTRACT

In the theory of curves, a magnetic field generates a magnetic flow whose trajectories
are curves, called magnetic curves.
In the present paper, magnetic curves which corresponding to killing magnetic fields of spherical
indicatrices for a regular curve in Euclidean 3-space are obtained. These curves are magnetic curves of the tangent, principal normal and binormal spherical indicatrices. Especially, for the tangent indicatrix of a regular curve, TT , NT and BT -magnetic curves are characterized. Furtheremore, some theorems and important results are given. Finally, we introduce an example to illustrate our main results with figures.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Topology & Geometry and Applications

11

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Linear one form deformation of sprays

Salah Gomma Ahmed Ali Elgendi

Faculty of Science - Benha University

ABSTRACT

In this paper, the linear one form deformation of a flat spray is investigated. The metrizability of the deformation
spray is characterized. New projectively flat Reimannain metrics are obtained. These new metrics are not,
generally, isometric to the Klein metric via affine transformations. New Finsler solutions for Hilbert's
fourth problem are constructed. Various examples are studied.