D.r.p. WİLLİAMS, K.b. LATHA, E. CH, E. CHANDRASEKERAN, - -

Fuzzy Bi-G-Ideals in G-Semigroups

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,

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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.