Abstract
In this paper, we introduce the concept of fuzzy generalized bi-ideal of a Γ-semigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γ-semigroup and characterize regular Γ-semigroups in terms of fuzzy generalized biideals.
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References
Chattopadhyay S (2001) Right inverse Γ-semigroup. Bulletin of Calcutta Mathematical Society 93: 435–442
Chattopadhyay S (2005) Right orthodox Γ-semigroup. South East Asian Bulletin of Mathematics 29: 23–30
Chinram R (2006) On quasi-Γ-ideals in Γ-semigroup. Science Asia 32: 351–353
Dutta T K, Adhikari N C (1993) On Γ-semigroup with right and left unities. Soochow Journal of Mathematics 19(4): 461–474
Dutta T K, Adhikari N C (1994) On prime radical of Γ-semigroup. Bulletin of Calcutta Mathematical Society 86(5): 437–444
Dutta T K, Sardar S K, Majumder S K (2009) Fuzzy ideal extensions of Γ-semigroups. International Mathematical Forum 4(42): 2093–2100
Dutta T K, Sardar S K, Majumder S K (2009) Fuzzy ideal extensions of Γ-semigroups via its operator semigroups. International Journal of Contemporary Mathematical Sciences 4(30): 1455–1463
Hila K (2008) On regular, semiprime and quasi-reflexive Γ-semigroup and minimal quasi-ideals. Lobachevskii Journal of Mathematics 29: 141–152
Hila K (2007) On some classes of le-Γ-semigroup. Algebras, Groups and Geometries 24: 485–495
Howie J M (1995) Fundamentals of semigroup theory. London Mathematical Society Monographs. New Series, 12. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York
Jun Y B, Hong S M, Meng J (1995) Fuzzy interior ideals in semigroups. Indian Journal of Pure Applied Mathematics 26(9): 859–863
Kuroki N (1981) On fuzzy ideals and fuzzy bi-ideals in semigroups. Fuzzy Sets and Systems 5: 203–215
Kuroki N (1991) On fuzzy semigroups. Information Sciences 53: 203–236
Kuroki N (1993) Fuzzy semiprime quasi-ideals in semigroups. Information Sciences 75(3): 201–211
Kuroki N (1992) Fuzzy generalized bi-ideals in semigroups. Information Sciences 66: 235–243
Mordeson et al (2003) Fuzzy semigroups. Springer-Verlag, Heidelberg
Rosenfeld A (1971) Fuzzy groups. J. Math. Anal. Appl. 35: 512–517
Sardar S K, Majumder S K (2009) On fuzzy ideals in Γ-semigroups. International Journal of Algebra 3(16): 775–784
Sardar S K, Majumder S K (2009) A note on characterization of prime ideals of Γ-semigroups in terms of fuzzy subsets. International Journal of Contemporary Mathematical Sciences 4(30): 1465–1472
Sardar S K, Majumder S K, Kayal S (2011) On fuzzy bi-ideals and fuzzy quasi-ideals in Γ-semigroups. “Vasile Alecsandri” University of Bacäu Faculty of Sciences Scientific Studies and Research Series Mathematics and Informatics 21(2): 135–156
Saha N K (1987) On Γ-semigroups II. Bulletin of Calcutta Mathematical Society 79: 331–335
Sen M K (1981) On Γ-semigroups. Proceedings of the International Conference on Algebra and its Application. Decker Publication, New York: 301–308
Sen M K, Saha N K (1986) On Γ-semigroups I. Bulletin of Calcutta Mathematical Society 78: 180–186
Seth A (1992) Γ-group congruences on regular Γ-semigroups. International Journal of Mathematics and Mathematical Sciences 15(1): 103–106
Xie X Y (2001) Fuzzy ideal extensions of semigroups. Soochow Journal of Mathematics 27(2): 125–138
Xie X Y (2005) Fuzzy ideal extensions of ordered semigroups. Lobach Journal of Mathematics 19: 29–40
Zadeh L A (1965) Fuzzy sets. Information and Control 8: 338–353
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Majumder, S.K., Mandal, M. Fuzzy generalized Bi-ideals of Γ-semigroups. Fuzzy Inf. Eng. 4, 389–399 (2012). https://doi.org/10.1007/s12543-012-0122-0
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DOI: https://doi.org/10.1007/s12543-012-0122-0