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http://dx.doi.org/10.14317/jami.2014.405

LA-SEMIGROUPS CHARACTERIZED BY THE PROPERTIES OF INTERVAL VALUED (α, β)-FUZZY IDEALS  

Abdullah, Saleem (Department of Mathematics, Quaid-i-Azam University)
Aslam, Samreen (Department of Mathematics, Quaid-i-Azam University)
Amin, Noor Ul (Department of Information Techology, Hazara University)
Publication Information
Journal of applied mathematics & informatics / v.32, no.3_4, 2014 , pp. 405-426 More about this Journal
Abstract
The concept of interval-valued (${\alpha},{\beta}$)-fuzzy ideals, interval-valued (${\alpha},{\beta}$)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Regular LA-semigroups are characterized by the properties of the lower part of interval-valued (${\in},{\in}{\vee}q$)-fuzzy left ideals, interval-valued (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and interval-valued (${\in},{\in}{\vee}q$)-fuzzy generalized bi-ideals. Main Facts.
Keywords
interval-valued (${\alpha},{\beta}$)-fuzzy sub LA-semigroups; interval-valued (${\alpha},{\beta}$)-fuzzy ideals; interval-valued (${\alpha},{\beta}$)-fuzzy bi-ideals; interval-valued (${\alpha},{\beta}$)-fuzzy quasi-ideals;
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1 Shabir, M., Jun, Y.B. and Nawaz, Y., 2010. Charaterization of regular semigroups by (${\alpha}$, ${\beta}$)-fuzzy ideals, Comput. Math. Appl., 59:161-175.   DOI   ScienceOn
2 Pu, M.A. and Liu, Y.M., 1980. Fuzzy topology 1, neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76:571-599.   DOI
3 Rosenfled, A., 1971. Fuzzy groups, J. Math. Anal. Appl., 35:512-517.   DOI
4 Shabir, M., and Khan, I.A., 2008. Interval-valued fuzzy ideals generated by an intervalvalued fuzzy subset in ordered semigroups, Math. Soft Comput., 15:263-272.
5 Shabir, M., Nawaz, Y. and Ali, M., 2011. Characterizations of semigroups by (${\overline{\in}}$,${\overline{\in}}$ ${\vee}$ ${\overline{q}}$)-fuzzy ideals, World Appl. Sci. J., 14(12):1866-1878.
6 Zadeh, L.A., 1965. Fuzzy sets, Inform. Control., 8:338-353.   DOI
7 Zadeh, L.A., 1975. The concept of a linguistic variable and its applications to approximate reasoning, Inform. Sci., 8:199-249.   DOI   ScienceOn
8 Zenab, R., 2009. Some studies in fuzzy AG-groupoids, M.phil Dissertation, Quaid-i-Azam University, Islamabad.
9 Zhan, J., Davvaz, B. and Shum, K.P., 2008. Generalized fuzzy hyperideals of hyperrings, Comput. Math. Appl., 56:1732-1740.   DOI   ScienceOn
10 Mushtaq, Q. and Yousaf, S.M., 1987. On LA-semigroups, The Alig. Bull. Math., 8:65-70.
11 Narayanan, A. and Manikantan, T., 2006. Interval-valued fuzzy ideals generated by an interval valued fuzzy subset in semigroups, J. App. Math & Comput., 20:455-464.   DOI
12 Bhakat, S.K. and Das, P., 1996. (${\in}$,${\in}$ ${\vee}$ q)-fuzzy subgroups, Fuzzy Sets and Systems, 80:359-368.   DOI   ScienceOn
13 Biwas, R., 1994. Rosenfeld's fuzzy subgroup with interval-valued membership functions, Fuzzy Sets and Systems, 63:87-90.   DOI   ScienceOn
14 Howie, J.M., 1995. Fundamentals of semigroup theory, Clarendon Press Oxford.
15 Murali, V., 2004. Fuzzy points of equivalent fuzzy subsets, Inform. Sci., 158:277-288.   DOI   ScienceOn
16 Kazim, M.A. and Naseerudin, M., 1972. On almost semigroups, The Alig. Bull. Math., 2:1-7.
17 Kuroki, N., 1992. Fuzzy bi-ideals in semigroups, Inform. Sci., 66:253-24.
18 Mordeson, J.N., Malik, D.S. and Kuroki, N., 2003. Fuzzy semigroups, Studies in Fuzziness and Soft Computing Vol. 131, Springer-Verlag Berlin.
19 Kazanci, O. and Yamak, S., 2008. Generalized fuzzy bi-ideals of semigroups, Soft Comput., 12(11):1119-1124.   DOI