Abstract
References
- Anthony, J. M. and Sherwood, H. Fuzzy groups redefined, J.Math. Anal. Appl. 69, 124–130, Barnes, W. E. On the Γ-rings of Nobusawa, Pacific J. Math. 18, 411–422, 1966.
- Booth, G. L. A note on Γ-nearrings, Stud. Sci. Hungarica 23, 471–475, 1988.
- Chinram R. Generalized transformation semigroups whose sets of quasi-ideals and bi–ideals coincide, Kyungpook Math. J. 45, 161–166, 2005.
- Chinram, R. and Jirojkul, C. On bi-Γ-ideals in Γ-semigroups, Songklanakarin J. Sci. Tech- nol. 29 (1), 231–234, 2007.
- Das, P. S. Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84, 264 -269, 1981.
- Dib, K. A. On Fuzzy spaces and Fuzzy group theory, Inform. Sci. 80, 253–282, 1994.
- Jun, Y. B. and Lee, C. Y. Fuzzy Γ-rings, Pusan Kyongnam Math. J. (presently, East Asian Math. J.) 8 (2), 163–170, 1992.
- Jun, Y. B., Sapanci, M. and Ozturk, M. A. Fuzzy ideals in gamma near-rings, Tr. J. of Mathematics 22, 449–459, 1998.
- Kuroki, N. Fuzzy bi–ideals in semigroups, Comment. Math. Univ. St. Paul. 28, 17–21, 1980.
- Kuroki, N. On Fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5, –215, 1981.
- Kyuno, S. On the radicals of Γ-rings, Osaka J. Math. 12, 639, 1975.
- Liu, W. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8, 133–139, Luh, J. On the theory of simple Γ-rings, Michigan Math. J. 16, 65, 1969.
- Mukerjee, N. P. and Bhattacharya, P. Fuzzy groups: some group theoretic analogs, Inform. Sci. 39, 247–268, 1986.
- Nobusawa, N. On generalization of the ring theory, Osaka J. Math. 1, 81–89, 1964.
- Ravisankar, T. S. and Shukla, U. S. Structure of Γ-rings, Pacific J. Math,80 (2), 537, 1979.
- Rosenfeld, A. Fuzzy groups, J. Math. Anal. Appl. 35, 512–517, 1971.
- Saha, N. K. On Γ-semigroup–II, Bull. Calcutta Math. Soc. 79 (6), 331–335, 1987.
- Saha, N. K. On Γ-semigroup–III, Bull. Calcutta Math. Soc. 80 (1), 1–12, 1988.
- Satyanarayana, Bh. Contributions to Near–ring Theory (Doctoral Thesis, Nagarjuna Uni- versity, 1984).
- Satyanarayana, Bh. A note on Γ-Near-rings, Indian J. Mathematics, bf41 (3), 427–433, 1999.
- Sen, M. K. and Saha, N. K., On Γ-semigroup–I, Bull. Calcutta Math. Soc. 78 (3), 180–186, Uckan, M., Mehmet, A. O. and Jun, Y. B. Intuitionistic fuzzy sets in Γ-semigroups, Bull. Korean Math. Soc. 44 (2), 359–367, 2007.
- Zadeh, L. A. Fuzzy sets, Information and Control, 8, 338–353, 1965.
Abstract
In this paper, we consider the fuzzification of bi-Γ-ideals in Γsemigroups, and investigate some of their related properties. Maximal fuzzy bi-Γ-ideals of Γ-semigroups are introduced and their properties discussed. Finally, chain conditions relating to fuzzy bi-Γ-ideals of Γsemigroups are investigated.
Keywords
Γ-semigroups Fuzzy Γ-ideals Fuzzy bi-Γ-ideals Fuzzy interior Γ-ideals 2000 AMS Classification: 20 M 99
References
- Anthony, J. M. and Sherwood, H. Fuzzy groups redefined, J.Math. Anal. Appl. 69, 124–130, Barnes, W. E. On the Γ-rings of Nobusawa, Pacific J. Math. 18, 411–422, 1966.
- Booth, G. L. A note on Γ-nearrings, Stud. Sci. Hungarica 23, 471–475, 1988.
- Chinram R. Generalized transformation semigroups whose sets of quasi-ideals and bi–ideals coincide, Kyungpook Math. J. 45, 161–166, 2005.
- Chinram, R. and Jirojkul, C. On bi-Γ-ideals in Γ-semigroups, Songklanakarin J. Sci. Tech- nol. 29 (1), 231–234, 2007.
- Das, P. S. Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84, 264 -269, 1981.
- Dib, K. A. On Fuzzy spaces and Fuzzy group theory, Inform. Sci. 80, 253–282, 1994.
- Jun, Y. B. and Lee, C. Y. Fuzzy Γ-rings, Pusan Kyongnam Math. J. (presently, East Asian Math. J.) 8 (2), 163–170, 1992.
- Jun, Y. B., Sapanci, M. and Ozturk, M. A. Fuzzy ideals in gamma near-rings, Tr. J. of Mathematics 22, 449–459, 1998.
- Kuroki, N. Fuzzy bi–ideals in semigroups, Comment. Math. Univ. St. Paul. 28, 17–21, 1980.
- Kuroki, N. On Fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems 5, –215, 1981.
- Kyuno, S. On the radicals of Γ-rings, Osaka J. Math. 12, 639, 1975.
- Liu, W. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8, 133–139, Luh, J. On the theory of simple Γ-rings, Michigan Math. J. 16, 65, 1969.
- Mukerjee, N. P. and Bhattacharya, P. Fuzzy groups: some group theoretic analogs, Inform. Sci. 39, 247–268, 1986.
- Nobusawa, N. On generalization of the ring theory, Osaka J. Math. 1, 81–89, 1964.
- Ravisankar, T. S. and Shukla, U. S. Structure of Γ-rings, Pacific J. Math,80 (2), 537, 1979.
- Rosenfeld, A. Fuzzy groups, J. Math. Anal. Appl. 35, 512–517, 1971.
- Saha, N. K. On Γ-semigroup–II, Bull. Calcutta Math. Soc. 79 (6), 331–335, 1987.
- Saha, N. K. On Γ-semigroup–III, Bull. Calcutta Math. Soc. 80 (1), 1–12, 1988.
- Satyanarayana, Bh. Contributions to Near–ring Theory (Doctoral Thesis, Nagarjuna Uni- versity, 1984).
- Satyanarayana, Bh. A note on Γ-Near-rings, Indian J. Mathematics, bf41 (3), 427–433, 1999.
- Sen, M. K. and Saha, N. K., On Γ-semigroup–I, Bull. Calcutta Math. Soc. 78 (3), 180–186, Uckan, M., Mehmet, A. O. and Jun, Y. B. Intuitionistic fuzzy sets in Γ-semigroups, Bull. Korean Math. Soc. 44 (2), 359–367, 2007.
- Zadeh, L. A. Fuzzy sets, Information and Control, 8, 338–353, 1965.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Article |
| Authors | |
| Publication Date | January 1, 2009 |
| IZ | https://izlik.org/JA35ZW66RW |
| Published in Issue | Year 2009 Volume: 38 Issue: 1 |