International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 7, Issue 2 (February 2020), Pages: 78-84

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 Original research Paper

 Title: Separation axioms on fuzzy ideal topological spaces in Šostak's sense

 Author(s): Fahad Alsharari 1, Yaser M. Saber 1, 2, *

 Affiliation(s):

 1Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia
 2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-4795-3469

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.02.011

 Abstract:

In the present paper, we introduce the notions of r-fuzzy *-open and r-fuzzy *-closed sets in Šostak's fuzzy topological spaces. Also, we study some properties of these notions. Moreover, we give the concept of fuzzy ideal *-irresolute mapping in Šostak's fuzzy topological spaces. Finally, we study some kinds of separation axioms namely r-FIRi where i={0.1.2.3} and r-FIRj  where j={1.2.2 1/2.3.4} and the relations between them. Also, some of their characterizations and several of fundamental properties have been established. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: r-fuzzy *-open, r-fuzzy *-closed, FI*-irresolute mapping, r-FIRi, r-FITj

 Article History: Received 11 September 2019, Received in revised form 15 December 2019, Accepted 17 December 2019

 Acknowledgment:

The authors would like to thank Deanship of Scientific Research at Majmaah University for supporting this work under Project Number No: R-1441-12. The authors would also like to express their sincere thanks to the referees for their useful suggestions and comments.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Alsharari F and Saber YM (2020). Separation axioms on fuzzy ideal topological spaces in Šostak's sense. International Journal of Advanced and Applied Sciences, 7(2): 78-84

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 References (20) 

  1. Alsharari F and Saber YM (2019). 𝒢Θτi⋆τ j-fuzzy closure operator. New Mathematics and Natural Computation. https://doi.org/10.1142/S1793005720500088   [Google Scholar]
  2. Chang CL (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24(1): 182-190. https://doi.org/10.1016/0022-247X(68)90057-7   [Google Scholar]
  3. Chattopadhyay KC and Samanta SK (1993). Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectedness. Fuzzy Sets and Systems, 54(2): 207-212. https://doi.org/10.1016/0165-0114(93)90277-O   [Google Scholar]
  4. Chattopadhyay KC, Hazra RN, and Samanta SK (1992). Gradation of openness: Fuzzy topology. Fuzzy Sets and Systems, 49(2): 237-242. https://doi.org/10.1016/0165-0114(92)90329-3   [Google Scholar]
  5. El Gayyar MK, Kerre EE, and Ramadan AA (1994). Almost compactness and near compactness in smooth topological spaces. Fuzzy Sets and Systems, 62(2): 193-202. https://doi.org/10.1016/0165-0114(94)90059-0   [Google Scholar]
  6. Hatir E and Jafari S (2007). Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization. Chaos, Solitons and Fractals, 34(4): 1220-1224. https://doi.org/10.1016/j.chaos.2006.03.116   [Google Scholar]
  7. Hohle U and Sostak P (1999). Axiomatic foundation of fixed-basis fuzzy topology. In: Hohle U and Rodabaugh SE (Eds.), The Handbooks of fuzzy sets series: Mathematics of fuzzy sets: 123-272. Volume 3, Springer, Boston, USA. https://doi.org/10.1007/978-1-4615-5079-2_5   [Google Scholar]
  8. Hutton B and Reilly I (1980). Separation axioms in fuzzy topological spaces. Fuzzy Sets and Systems, 3(1): 93-104. https://doi.org/10.1016/0165-0114(80)90007-X   [Google Scholar]
  9. Kim YC and Ko JM (2001). Fuzzy semi-regular spaces and fuzzy δ-continuous functions. International Journal of Fuzzy Logic and Intelligent Systems, 1(1): 69-74.   [Google Scholar]
  10. Lowen R (1976). Fuzzy topological spaces and fuzzy compactness. Journal of Mathematical Analysis and Applications, 56(3): 621-633. https://doi.org/10.1016/0022-247X(76)90029-9   [Google Scholar]
  11. Nasef AA and Mahmoud RA (2002). Some topological applications via fuzzy ideals. Chaos, Solitons and Fractals, 13(4): 825-831. https://doi.org/10.1016/S0960-0779(01)00058-3   [Google Scholar]
  12. Pao-Ming P and Ying-Ming L (1980). Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Applications, 76(2): 571-599. https://doi.org/10.1016/0022-247X(80)90048-7   [Google Scholar]
  13. Ramadan AA (1992). Smooth topological spaces. Fuzzy Sets and Systems, 48(3): 371-375. https://doi.org/10.1016/0165-0114(92)90352-5   [Google Scholar]
  14. Ramadan AA, Abbas SE, and Kim YC (2001). Fuzzy irresolute mappings in smooth fuzzy topological spaces. Journal of Fuzzy Mathematics, 9(4): 865-878.   [Google Scholar]
  15. Saber YM and Abdel-Sattar MA (2014). Ideals on fuzzy topological spaces. Applied Mathematical Sciences, 8(34): 1667-1691. https://doi.org/10.12988/ams.2014.33194   [Google Scholar]
  16. Saber YM and Alsharari F (2018). Generalized fuzzy ideal closed sets on fuzzy topological spaces in Sostak sense. International Journal of Fuzzy Logic and Intelligent Systems, 18(3): 161-166. https://doi.org/10.5391/IJFIS.2018.18.3.161   [Google Scholar]
  17. Sarkar D (1997). Fuzzy ideal theory fuzzy local function and generated fuzzy topology. Fuzzy Sets and Systems, 87(1): 117-123. https://doi.org/10.1016/S0165-0114(96)00032-2   [Google Scholar]
  18. Šostak A (1989). On some modifications of fuzzy topology. Matematički Vesnik, 41(104): 51-64.   [Google Scholar]
  19. Šostak AP (1985). On a fuzzy topological structure. In the 13th Winter School on Abstract Analysis, Circolo Matematico di Palermo, Palermo, Italy: 89-103.   [Google Scholar]
  20. Zahran AM, Abbas SE, El-baki SA, and Saber YM (2009). Decomposition of fuzzy continuity and fuzzy ideal continuity via fuzzy idealization. Chaos, Solitons and Fractals, 42(5): 3064-3077. https://doi.org/10.1016/j.chaos.2009.04.010   [Google Scholar]