New Generalized Definitions of Rough Membership Relations and Functions from Topological Point of View

Authors

  • Mostafa Kamel El-Bably Dr. Mostafa K. El-Bably *Lecturer of Mathematics, Deanery of Academic Services, Taibah University (Al-Ula Gov.), Al-Madinah Al-Munawwara,Saudi Arabia. *Department of Mathematics, *Faculty of Science, Tanta University, EGYPT. *Member of Egyptian Mathematics Society (ETMS). *Present address: 3, Al-Malk Fahd St., P.O.Box 567, Al-Ula 41921 Saudi Arabia.
  • A.M. Kozae Prof. Dr. of Mathematics Department of Mathematics Faculty of Science Tanta University, EGYPT.
  • M. E. Abd El-Monsef Prof. Dr. of Mathematics Department of Mathematics Faculty of Science Tanta University, EGYPT.

DOI:

https://doi.org/10.24297/jam.v8i3.2575

Keywords:

j-Neighborhood Space, Topology, Near Operators, Membership Relations, Rough Set, Membership Functions and Fuzzy Set.

Abstract

In this paper, we shall integrate some ideas in terms of concepts in topology. In fact, we introduce two different views to define generalized membership relations and functions as mathematical tools to classify the sets and help for measuring exactness and roughness of sets. Moreover, we define several types of fuzzy sets. Comparisons between the induced operations were discussed. Finally, many results, examples and counter examples to indicate connections are investigated.

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Author Biographies

  • Mostafa Kamel El-Bably, Dr. Mostafa K. El-Bably *Lecturer of Mathematics, Deanery of Academic Services, Taibah University (Al-Ula Gov.), Al-Madinah Al-Munawwara,Saudi Arabia. *Department of Mathematics, *Faculty of Science, Tanta University, EGYPT. *Member of Egyptian Mathematics Society (ETMS). *Present address: 3, Al-Malk Fahd St., P.O.Box 567, Al-Ula 41921 Saudi Arabia.
    Department of Mathematics,
    *Faculty of Science, Tanta University, EGYPT.  
    *Member of Egyptian Mathematics Society (ETMS).

  • A.M. Kozae, Prof. Dr. of Mathematics Department of Mathematics Faculty of Science Tanta University, EGYPT.
    Prof. Dr. of Mathematics
    Department of Mathematics
    Faculty of Science
    Tanta University, EGYPT.
  • M. E. Abd El-Monsef, Prof. Dr. of Mathematics Department of Mathematics Faculty of Science Tanta University, EGYPT.
    Department of Mathematics
    Faculty of Science
    Tanta University, EGYPT.
JOURNAL OF ADVANCES IN MATHEMATICS

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Published

2014-05-24

Issue

Vol. 8 No. 3 (2014)

Section

Articles

License

Creative Commons License All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

New Generalized Definitions of Rough Membership Relations and Functions from Topological Point of View. (2014). JOURNAL OF ADVANCES IN MATHEMATICS, 8(3), 1635-1652. https://doi.org/10.24297/jam.v8i3.2575

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