Volume 7, Issue 7 (July 2020), Pages: 75-82

----------------------------------------------

 Original Research Paper

 Title: A study on ordered AG-groupoids by their fuzzy interior ideals

 Author(s): Nasreen Kausar ^1, *, Meshari Alesemi ², Salahuddin ², Mohammad Munir ³

 Affiliation(s):

 ¹Department of Math and Stat, University of Agriculture Faisalabad, Faisalabad, Pakistan
 ²Department of Mathematics, Jazan University, Jazan, Saudi Arabia
 ³Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-8659-0747

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.07.009

 Abstract:

The purpose of this paper is to study the different classes of ordered AG-groupoids by using fuzzy left (resp. right, interior) ideals. Particularly, we illustrate regular (resp. right regular, left regular, (2, 2)-regular, weakly regular and intra-regular) ordered AG-groupoids in terms of fuzzy left (resp. right, interior) ideals. In this regard, we show that in (regular, right regular, weakly regular) ordered AG-groupoids, the concept of fuzzy (interior, two-sided) ideals coincide. The concept of fuzzy (interior, two-sided) ideals coincide in ((2,2), left, intra-) regular ordered AG-groupoids with left identity. 

 © 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: Fuzzy left ideal, Fuzzy right ideal, Fuzzy interior ideals, Regular ordered AG-groupoid

 Article History: Received 23 December 2019, Received in revised form 2 April 2020, Accepted 20 April 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

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

 Citation:

 Kausar N, Alesemi M, and Salahuddin et al. (2020). A study on ordered AG-groupoids by their fuzzy interior ideals. International Journal of Advanced and Applied Sciences, 7(7): 75-82

 Permanent Link to this page

 Figures

 No Figure

 Tables

 No table

----------------------------------------------

 References (10)

1. Dib KA and Galhum N (1997). Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups. Fuzzy Sets and Systems, 92(1): 103-111. https://doi.org/10.1016/S0165-0114(96)00170-4   [Google Scholar]
2. Holgate P (1992). Groupoids satisfying a simple invertive law. Mathematical Study, 61(1-4): 101-106. https://doi.org/10.1007/BF00163844   [Google Scholar]
3. Kazim MA and Naseeruddin M (1977). On almost semigroups. Portugaliae Mathematica 36(1): 41-47.   [Google Scholar]
4. Kehayopulu N and Tsingelis M (2002). Fuzzy sets in ordered groupoids. Semigroup Forum, 65: 128-132. https://doi.org/10.1007/s002330010079   [Google Scholar]
5. Kuroki N (1995). Fuzzy interior ideals in semigroups. The Journal of Fuzzy Mathematics, 3(2): 435-447.   [Google Scholar]
6. Mordeson JN, Malik DS, and Kuroki N (2003). Fuzzy semigroups. Springer, Berlin, Germany. https://doi.org/10.1007/978-3-540-37125-0   [Google Scholar]
7. Mushtaq Q and Yusuf SM (1978). On LA-semigroups. The Aligarh Bulletin of Mathematics, 8: 65-70.
8. Rosenfeld A (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3): 512-517. https://doi.org/10.1016/0022-247X(71)90199-5   [Google Scholar]
9. Shah T and Kausar N (2014). Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals. Theoretical Computer Science, 529: 96-110. https://doi.org/10.1016/j.tcs.2014.02.007   [Google Scholar]
10. Zadeh LA (1965). Fuzzy sets. Information and Control, 8(3): 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X   [Google Scholar]