Abstract
In this paper, we introduce and use the concept of \((\in _{\gamma },\in _{\gamma }\vee q_{\delta })\)-fuzzy soft right ideals, to study the structural properties of an \(\mathcal {AG}\)-groupoid. We characterize an intra-regular \(\mathcal {AG}\)-groupoids using the properties of \((\in _{\gamma },\in _{\gamma }\vee q_{\delta })\)-fuzzy soft sets and \((\in _{\gamma },\in _{\gamma }\vee q_{\delta })\)-fuzzy soft right ideals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhakat, S.K., Das, P.: On the definition of a fuzzy subgroup. Fuzzy Sets Syst. 51, 235–241 (1992)
Bhakat, S.K., Das, P.: \((\in,\in \vee _{q})\)-fuzzy subgroups. Fuzzy Sets Syst. 80, 359368 (1996)
Feng, F., Jun, Y.B., Zhao, X.: Soft semirings. Comput. Math. Appl. 56, 2621–2628 (2008)
Feng, F., Li, Y.M.: Soft subsets and soft product operations. Inf. Sci. 232, 44–57 (2013)
Irfan Ali, M., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)
Jun, Y.B.: Soft BCK/BCI-algebras. Comput. Math. Appl. 56, 1408–1413 (2008)
Kazim, M.A., Naseeruddin, M.: On almost semigroups. The Allig. Bull. Math. 2, 1–7 (1972)
Molodstov, D.: Soft set theory first-results. Comput. Math. Appl. 37(4-5), 19–31 (1999)
Modeson, J.N., Malik, D.S., Kuroki, N.: Fuzzy Semigroups. Springer, Berlin (2003)
Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)
Murali, V.: Fuzzy points of fuzzy equivalent fuzzy subsets. Inf. Sci. 158, 277–288 (2004)
Mushtaq, Q., Yousuf, S.M.: On LA-semigroups. Alig. Bull. Math. 8, 65–70 (1978)
Pu, P.M., Liu, Y.M.: Fuzzy topology I, neighborhood structure of a fuzzy point and Mooresmith convergence. J. Math. Anal. Appl. 76, 571–599 (1980)
Shabir, M., Jun, Y.B., Nawas, Y.: Semigroups characterized by \((\in,\in \vee _{qk})\)-fuzzy bi-ideals. Comput. Math. Appl. 60, 1473–1493 (2010)
Shabir, M., Jun, Y.B., Nawas, Y.: Characterizations of regular semigroups by \((\alpha,\beta )\)-fuzzy ideals. Comput. Math. Appl. 59, 161–175 (2010)
Yin, Y., Zhan, J.: Characterization of ordered semigroups in terms of fuzzy soft ideals. Bull. Malays. Math. Sci. Soc. (2). 35(4), 997–1015 (2012)
Zadeh, L.A.: Fuzzy sets. J. Inf. Sci. 8, 338–353 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ali, A., Khan, M. & Shi, FG. On fuzzy soft intra-regular Abel–Grassmann’s groupoids. Afr. Mat. 28, 171–187 (2017). https://doi.org/10.1007/s13370-016-0435-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-016-0435-y
Keywords
- \(\mathcal {AG}\)-Groupoid
- Left invertve law
- Medial law
- Paramedial law
- \(({\in }_{\gamma }, {\in }_{\gamma }\vee q_{\delta })\)-Fuzzy soft set and \(({\in }_{\gamma }, {\in }_{\gamma }\vee q_{\delta })\)-Fuzzy soft right ideal