Retract Neutrosophic Crisp Information Systems

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Presentation transcript:

Retract Neutrosophic Crisp Information Systems A.A.Salama2, Hewayda ElGhawalby1 and Asmaa.M.Nasr1 1 Port Said University, Faculty of Engineering, Physics and Engineering MathematicsDepartment, Egypt. somanasr06@gmail.com hewayda2011@eng.psu.edu.eg 2Port Said University, Faculty of Science, Department of Mathematics and Computer Science, Egypt. drsalama44@gmail.com

Abstract In this paper, we aim to develop a new type of neutrosophic crisp set called the retract neutrosophic crisp set. The introduced set is a retraction of any triple structured crisp set. Whereas, the retract set deduced from any neutrosophic crisp set is coincide its corresponding star neutrosophic crisp set defined in by Salama et al. [6]. Hence we construct a new type of neutrosophic crisp topological spaces, called the retract neutrosophic crisp topological space as a retraction of the star neutrosophic topological space. Moreover, we investigate some of its properties. Possible applications to nursing data research are touched upon.

Introduction: Crisp Set Intuitionistic Crisp Set . Neutrosophic Crisp Set Star Neutrosophic Crisp Set Retract Neutrosophic Crisp Set

U (Universe of discourse) Crisp Sets A crisp set (an ordinary or a classical set) is defined in such a way that all the individuals in a given universe can be partitioned into two classes: those who belong to the set, and those who do not belong to the set. U (Universe of discourse)

Intuitionistic Crisp Set

Neutrosophic Crisp Sets

Definition The object having the form can be classified into three different classes as follows: (a) A, is said to be neutrosophic crisp set of class 1 (NCS-Class1) if satisfying:

Definition The object having the form can be classified into three different classes as follows: (b) A, is said to be neutrosophic crisp set of class 2 (NCS-Class2) if satisfying:

Definition The object having the form can be classified into three different classes as follows: (c) A, is said to be neutrosophic crisp set of class 3 (NCS-Class3) if satisfying:

Star Neutrosophic Crisp Sets

Retract Neutrosophic Crisp Set

Definition

Retract Neutrosophic Crisp Topological Spaces

Remarks

Definition

Proposition

Definition

Thank you