Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals

Full Text (PDF, 384KB), PP.1-8

Views: 0 Downloads: 0

Author(s)

A. A. Salama 1,* Said Broumi 2 Florentin Smarandache 3

1. Department of Mathematics and Computer Science, Faculty of Sciences, Port Said University, 23 December Street, Port Said 42522, Egypt

2. Faculty of Arts and Humanities, Hay El Baraka Ben M'sik Casablanca B.P. 7951, Hassan II University Mohammedia- Casablanca, Morocco

3. Department of Mathematics, University of New Mexico,705 Gurley Avenue, Gallup, NM 87301, USA

* Corresponding author.

DOI: https://doi.org/10.5815/ijieeb.2014.03.01

Received: 26 Feb. 2014 / Revised: 12 Apr. 2014 / Accepted: 2 May 2014 / Published: 8 Jun. 2014

Index Terms

Neutrosophic Crisp Set, Neutrosophic Crisp Ideals, Neutrosophic Crisp L-open Sets, Neutrosophic Crisp L- Continuity, Neutrosophic Sets

Abstract

The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp L- continuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic crisp functions.

Cite This Paper

A. A. Salama, Said Broumi, Florentin Smarandache, "Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.6, no.3, pp.1-8, 2014. DOI:10.5815/ijieeb.2014.03.01

Reference

[1]K. Atanassov, intuitionistic fuzzy sets, in V.Sgurev, ed., Vii ITKRS Session, Sofia (June 1983 central Sci. and Techn. Library, Bulg. Academy of Sciences (1984).

[2]K. Atanassov, intuitionistic fuzzy sets, Fuzzy Sets and Systems 20, (1986),pp. 87-96.

[3]K. Atanassov, Review and new result on intuitionistic fuzzy sets, preprint IM-MFAIS-Sofia, (1988), pp.1-88.

[4]S. A. Alblowi, A.A.Salama and Mohmed Eisa, New Concepts of Neutrosophic Sets, International Journal of Mathematics and Computer Applications Research (IJMCAR),Vol. 4, Issue 1, (2014),pp. 59-66.

[5]I. Hanafy, A.A. Salama and K. Mahfouz, Correlation of Neutrosophic Data, International Refereed Journal of Engineering and Science (IRJES), Vol.(1), Issue 2 .(2012), pp.33-39.

[6]I.M. Hanafy, A.A. Salama and K.M. Mahfouz,," Neutrosophic Classical Events and Its Probability" International Journal of Mathematics and Computer Applications Research(IJMCAR) Vol.(3),Issue 1, (2013), pp.171-178.

[7]A. A. Salama and S.A. Alblowi, "Generalized Neutrosophic Set and Generalized Neutrosophic Spaces,"Journal Computer Sci. Engineering, Vol. (2) No. (7) (2012),pp.129-132.

[8]A. A. Salama and S. A. Alblowi, Neutrosophic Set and Neutrosophic Topological Spaces, ISOR J. Mathematics, Vol.(3), Issue(3), (2012), pp-31-35.

[9]A. A. Salama, "Neutrosophic Crisp Point & Neutrosophic Crisp Ideals", Neutrosophic Sets and Systems, Vol.1, No. 1, (2013), pp. 50-54.

[10]A. A. Salama and F. Smarandache, "Filters via Neutrosophic Crisp Sets", Neutrosophic Sets and Systems, Vol.1, No. 1, (2013), pp. 34-38.

[11]A.A. Salama and S.A. Alblowi, Intuitionistic Fuzzy Ideals Spaces, Advances in Fuzzy Mathematics , Vol.(7), Number 1, (2012) pp. 51- 60.

[12]A.A. Salama, and H.Elagamy, "Neutrosophic Filters" International Journal of Computer Science Engineering and Information Technology Reseearch (IJCSEITR), Vol.3, Issue(1),Mar 2013,(2013), pp. 307-312.

[13]A. A. Salama, F.Smarandache and Valeri Kroumov "Neutrosophic crisp Sets & Neutrosophic crisp Topological Spaces" Bulletin of the Research Institute of Technology (Okayama University of Science, Japan), in January-February (2014). (Accepted).

[14]A. A. Salama, Mohamed Eisa and M. M . Abdelmoghny, "Neutrosophic Relations Database" International Journal of Information Science and Intelligent System, 3(1) (2014).

[15]A. A. Salama, Florentin Smarandache and S. A. ALblowi, New Neutrosophic Crisp Topological Concepts, Neutrosophic Sets and Systems, Vol.2, No. 1, (2014).

[16]Florentin Smarandache, Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy , Neutrosophic Logic, Set, Probability, and Statistics University of New Mexico, Gallup, NM 87301, USA(2002).

[17]F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic crisp Set, Neutrosophic Probability. American Research Press, Rehoboth, NM, (1999).

[18]F. Smarandache, Neutrosophic set, a generialization of the intuituionistics fuzzy sets, Inter. J. Pure Appl. Math., 24 (2005), pp.287 – 297.

[19]Debasis Sarker, Fuzzy ideal theory, Fuzzy local function and generated fuzzy topology, Fuzzy Sets and Systems 87, (1997),pp.117 – 123.

[20]L.A. Zadeh, Fuzzy Sets, Inform and Control 8, ,(1965),pp.338-353.