Anti fuzzy bi-ideals on ordered AG-groupoids

Nasreen Kausar; Mohammad Munir; Muhammad Gulzar; Gezahagne Mulat Addis; Rukhshanda Anjum

doi:10.22342/jims.26.3.862.299-318

Nasreen Kausar ⁽¹⁾ , Mohammad Munir ⁽²⁾ , Muhammad Gulzar ⁽³⁾ , Gezahagne Mulat Addis ⁽⁴⁾ , Rukhshanda Anjum ⁽⁵⁾

(1) Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan,

(2) Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan,

(3) Department of Mathematics, Government College University Faisalabad, Pakistan,

(4) Department of Mathematics, University of Gondar, Gondar, Ethiopia,

(5) Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

https://doi.org/10.22342/jims.26.3.862.299-318

Issue
VOLUME 26 NUMBER 3 (NOVEMBER 2020)

Submitted
July 13, 2019

Accepted
April 13, 2020

Published
November 5, 2020

Keywords:

Fuzzy sets, anti fuzzy AG-subgroupoids, anti fuzzy left (resp. right, bi-, generalized bi-, (1, 2)-) ideals. 2010 MSC, 03F55, 08A72, 20N25

PDF

Abstract

The purpose of this study is to initiate the notion of anti fuzzy left (resp. right, bi-, generalized bi-, (1,2)-) ideals in non-associative and non-commutative ordered semigroups. We characterize different classes of non-associative and non-commutative ordered semigroups in terms of such ideals.

Full text article

Generated from XML file

References

M. Akram and K. H. Dar, On anti fuzzy left h-ideals in hemirings, Int. Math. Forum, 2(2007) 2295-2304.

N. Kausar, M. Waqar, Characterizations of non-associative rings by their intuitionistic fuzzy bi-ideals, European Journal of Pure and Applied Mathematics, Vol. 12, 1(2019) 226-250.

N. Kausar, Characterizations of non-associative ordered semigroups by the properties of their fuzzy ideals with thresholds (α; β]; Prikladnaya Diskretnaya Matematika, Vol. 43(2019) 37-

N. Kausar, Direct product of finite intuitionistic anti fuzzy normal subrings over nonassociative rings, European Journal of Pure and Applied Mathematics, Vol. 12, 2(2019) 622-648.

N. Kausar, B. Islam, M. Javaid, S, Amjad, U. Ijaz, Characterizations of non-associative rings

by the properties of their fuzzy ideals, Journal of Taibah University for Science, Vol. 13, 1(2019) 820-833.

N. Kausar, B. Islam, S. Amjad, M. Waqar, Intuitionistics fuzzy ideals with thresholds (α; β] in LA-rings, European Journal of Pure and Applied Mathematics, Vol. 12, 3(2019) 906-943.

N. Kausar, M. Waqar, Direct product of finite fuzzy normal subrings over non-associative rings, International Journal of Analysis and Applications, Vol. 17, 5(2019) 752-770.

N. Kausar, M. Alesemi, Salahuddin, Anti fuzzy interior ideals on Ordered AG-groupoids, European Journal of Pure and Applied Mathematics, Vol. 13, 1(2020) 113-129.

N. Kausar, Meshari Alesemi, Salahuddin, Fuzzy ideals on ordered AG-groupoids", International Journal of Analysis and Applications, Vol. 18, 2(2020) 277-303.

N. Kausar, Meshari Alesemi, Salahuddin, Mohammad Munir Characterizations of nonassociative ordered semigroups by their intuitionistic fuzzy bi-ideals, Discontinuity, Nonlinearity, and Complexity Vol. 9, 2(2020) 257-275.

M Kaviyarasu, K Indhira, VM Chandrasekaran, Fuzzy sub algebras and Fuzzy K-ideals in INK-algebras, International Journal of Pure and Applied Mathematics, vol. 113, 6(2017) 47-55.

M Kaviyarasu, K Indhira, VM Chandrasekaran, Direct Product of Intuitionistic Fuzzy KIdeals of INK-Algebras, Materials Today: Proceedings, vol. 16(2019) 449-455.

M. A. Kazim and M. Naseerudin, On almost semigroups, Alig. Bull. Math., 2(1972) 1-7.

N. Kehayopulu, On intra-regular ordered semigroups, Semigroup Forum, 46(1993) 271-278.

N. Kehayopulu and M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum, 65(2002) 128-132.

N. Kuroki, On fuzzy semigroups, Inform. Sci., 5(1991) 203-36.

S. K. Majumder and S. K. Sardar, On some properties of anti fuzzy subgroups, J. Mech. Cont. Math. Sci., 3(2008) 337-343.

A. Al-Masarwah and A.G. Ahmad, m-Polar fuzzy ideals of BCK/BCI-algebras. J. King Saud Univ.-Sci., Vol. 31 4(2019) 1220-1226.

A. Al-Masarwah and A.G. Ahmad, On (complete) normality of m-pF subalgebras in BCK/BCI-algebras, AIMS Mathematics Vol. 4, 3(2019) 740-750.

A. Al-Masarwah and A.G. Ahmad, On some properties of doubt bipolar fuzzy H-ideals in BCK/BCI-algebras. Eur. J. Pure Appl. Math. Vol. 11, 3(2018) 652-670.

A. Al-Masarwah and A.G. Ahmad, Doubt bipolar fuzzy subalgebras and ideals in BCK/BCIalgebras. J. Math. Anal. Vol. 9, 3(2018) 9-27.

A. Al-Masarwah and A.G. Ahmad, Novel concepts of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras. Int. J. Innov. Comput. Inf. Control. Vol. 14, 6(2018) 2025-2041.

J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy semigroups, Springer, Berlin, (2003).

M. Abu. Qamar and N. Hassan, An approach toward a Q-neutrosophic soft set and its application in decision making, Symmetry, Vol. 11, 2(2019), 139.

M. Abu. Qamar and N. Hassan, Q-neutrosophic soft relation and its application in decision making, Entropy, Vol. 20, 3(2018), 172.

T. Shah, N. Kausar and I. Rehman, Intuitionistic fuzzy normal subrings over a non-associative ring, An. St. Univ. Ovidius Constanta, Vol. 20(2012) 369-386.

T. Shah and N. Kausar, Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theoretical Computer Science, Vol. 529(2014) 96-110.

L. A. Zadeh, Fuzzy sets, Information and control, Vol. 8(1965) 338-363.

Authors

Nasreen Kausar

Department of Mathematics and Statistics, University of Agriculture, Faisalabad

kausar.nasreen57@gmail.com (Primary Contact)

Mohammad Munir

Department of Mathematics, Government Postgraduate College, Abbottabad

Muhammad Gulzar

Department of Mathematics, Government College University Faisalabad

Gezahagne Mulat Addis

Department of Mathematics, University of Gondar, Gondar

Rukhshanda Anjum

Department of Mathematics and Statistics, University of Lahore, Lahore

Author Biography

Nasreen Kausar, Department of Mathematics and Statistics, University of Agriculture, Faisalabad

Mathematics

Assistant Professor

Kausar, N., Munir, M., Gulzar, M., Addis, G. M., & Anjum, R. (2020). Anti fuzzy bi-ideals on ordered AG-groupoids. Journal of the Indonesian Mathematical Society, 26(3), 299–318. https://doi.org/10.22342/jims.26.3.862.299-318