On Generalized Fuzzy Interior Ideals in G-Semigroups

Year 2012, Volume: 41 Issue: 2, 231 - 241, 01.02.2012

S.k. Sardar B. Davvaz S.k. Majumder S. Kayal

https://izlik.org/JA67GM95GE

Keywords

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References

• Adhikari, N. C. Study of some problems associated with Γ-Semigroups (Ph.D. Dissertation, University of Calcutta, 1998).
• Bhakat, S. K. and Das, P. On the definition of a fuzzy subgroup, Fuzzy Sets and Systems , 235–241, 1992.
• Bhakat, S. K. and Das, P. (∈, ∈ ∨q)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996) –368, 1996.
• Chattopadhyay, S. Right inverse Γ-semigroup, Bull. Cal. Math. Soc. 93, 435–442, 2001.
• Chattopadhyay, S. Right orthodox Γ-semigroup, Southeast Asian Bull. Math. 29, 23–30, Chinram, R. On quasi-Γ-ideals in Γ-semigroups, Science Asia 32, 351–353, 2006.
• Dutta, T. K. and Adhikari, N. C. On Γ-semigroup with the right and left unities, Soochow J. Math. 19 (4), 461–474, 1993.
• Dutta, T. K. and Adhikari, N. C. On prime radical of Γ-semigroup, Bull. Cal. Math. Soc. (5), 437–444, 1994.
• Dutta, T. K., Sardar, S. K. and Majumder, S. K. Fuzzy ideal extensions of Γ-semigroups, International Mathematical Forum 4 (41), 2093–2100, 2009.
• Dutta, T. K., Sardar, S. K. and Majumder, S. K. Fuzzy ideal extensions of Γ-semigroups via its operator semigroups, Int. J. Contemp. Math. Sciences 4 (30), 1455–1463, 2009.
• Hila, K. On regular, semiprime and quasi-reflexive Γ-semigroup and minimal quasi-ideals, Lobachevski J. Math. 29, 141–152, 2008.
• Hila, K. On some classes of le-Γ-semigroup and minimal quasi-ideals, Algebras Groups Geom. 24, 485–495, 2007.
• Huang, X. and Yin, Y. The (∈, ∈ ∨q)-Fuzzy prime ideals and maximal ideals of a semigroup, International Mathematical Forum 3 (39), 1915–1932, 2008.
• Jun, Y. B. and Song, S. Z. Generalized fuzzy interior ideals in semigroups, Inform Sci. 176, –3093, 2006.
• Kuroki, N. On fuzzy semigroups, Inform Sci. 53, 203–236, 1991.
• Kuroki, N. On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5, –215, 1981.
• Kuroki, N. Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems 158, 277–288, Murali, V. Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158, 277–288, 2004.
• Pu, P. M. and Liu, Y. M. Fuzzy topology I, neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980.
• Rosenfeld, A. Fuzzy groups, J. Math. Anal. Appl. 35, 512–517, 1971.
• Saha, N. K. On Γ-semigroup II, Bull. Cal. Math. Soc. 79, 331–335, 1987.
• Sardar, S. K. and Majumder, S. K. On fuzzy ideals in Γ-semigroups, International Journal of Algebra 3 (16), 775–784, 2009.
• Sardar, S. K., Majumder, S. K. and Mandal, D. A note on characterization of prime ideals of Γ-semigroups in terms of fuzzy subsets, Int. J. Contemp. Math. Sciences 4 (30), 1465–1472,
• Sardar, S. K. and Majumder, S. K. A note on characterization of semiprime ideals of Γ- semigroups in terms of fuzzy subsets, International Journal of Pure and Applied Mathemat- ics 3 (56), 451–457, 2009.
• Sardar, S. K., Davvaz, B. and Majumder, S. K. A study on fuzzy interior ideals of Γ- semigroups, Computers and Mathematics with Applications 60, 90–94, 2010.
• Sardar, S. K., Davvaz, B., Majumder, S. K. and Kayal, S. On generalised fuzzy subsemigroup and generalized fuzzy bi-ideal inΓ-semigroups, communicated. Sardar, S. K., Davvaz, B., Majumder, S. K. and Kayal, S. A note on generalised fuzzy ideals inΓ-semigroups, preprint. Sardar, S. K., Majumder, S. K. and Kayal, S. On fuzzy bi-ideals and fuzzy quasi ideals in Γ-semigroups, communicated. Sen, M. K. and Chattopadhyay, S. Semidirect product of a monoid and a Γ-semigroup, East-West J. Math. 6, 131–138, 2004.
• Sen, M. K. and Saha, N. K. Orthodox Γ-semigroups, Internat. J. Math. Math. Sci. 13, 527– , 1990.
• Sen, M. K. and Saha, N. K. On Γ-semigroup I, Bull. Cal. Math. Soc. 78, 180–186, 1986.
• Seth, A. Γ-group congruences on regular Γ-semigroups, Internat. J. Math. Math. Sci. 15, –106, 1992.
• Uckun, M., ¨Ozt¨urk, M. A. and Jun, Y. B. Intuitionistic fuzzy sets in Γ-semigroups, Bull. Korean Math. Soc. 44 (2), 359–367, 2007.
• Yuan, X., Zhang, C. and Ren, Y. Generalized fuzzy groups and many-valued implications, Fuzzy Sets and Systsems 138, 205–211, 2003.
• Yunqiang, Y., Xu, D. and Li, H. The (∈, ∈ ∨q)-fuzzy subsemigroups and ideals of an (∈, ∈ ∨q)-fuzzy semigroup, Southeast Asian Bull. Math. 33, 391–400, 2009.
• Zadeh, L. A. Fuzzy Sets, Information and Control 8, 338–353, 1965.