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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

Keywords

-

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.

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

Keywords

-

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.
There are 31 citations in total.

Details

Primary Language Turkish
Authors

S.k. Sardar This is me

B. Davvaz This is me

S.k. Majumder This is me

S. Kayal This is me

Publication Date February 1, 2012
Published in Issue Year 2012 Volume: 41 Issue: 2

Cite

APA Sardar, S., Davvaz, B., Majumder, S., Kayal, S. (2012). On Generalized Fuzzy Interior Ideals in G-Semigroups. Hacettepe Journal of Mathematics and Statistics, 41(2), 231-241.
AMA Sardar S, Davvaz B, Majumder S, Kayal S. On Generalized Fuzzy Interior Ideals in G-Semigroups. Hacettepe Journal of Mathematics and Statistics. February 2012;41(2):231-241.
Chicago Sardar, S.k., B. Davvaz, S.k. Majumder, and S. Kayal. “On Generalized Fuzzy Interior Ideals in G-Semigroups”. Hacettepe Journal of Mathematics and Statistics 41, no. 2 (February 2012): 231-41.
EndNote Sardar S, Davvaz B, Majumder S, Kayal S (February 1, 2012) On Generalized Fuzzy Interior Ideals in G-Semigroups. Hacettepe Journal of Mathematics and Statistics 41 2 231–241.
IEEE S. Sardar, B. Davvaz, S. Majumder, and S. Kayal, “On Generalized Fuzzy Interior Ideals in G-Semigroups”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 231–241, 2012.
ISNAD Sardar, S.k. et al. “On Generalized Fuzzy Interior Ideals in G-Semigroups”. Hacettepe Journal of Mathematics and Statistics 41/2 (February2012), 231-241.
JAMA Sardar S, Davvaz B, Majumder S, Kayal S. On Generalized Fuzzy Interior Ideals in G-Semigroups. Hacettepe Journal of Mathematics and Statistics. 2012;41:231–241.
MLA Sardar, S.k. et al. “On Generalized Fuzzy Interior Ideals in G-Semigroups”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, 2012, pp. 231-4.
Vancouver Sardar S, Davvaz B, Majumder S, Kayal S. On Generalized Fuzzy Interior Ideals in G-Semigroups. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):231-4.

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