**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30843

##### A Note on Characterization of Regular Γ-Semigroups in terms of (∈,∈ ∨q)-Fuzzy Bi-ideal

**Authors:**
S.K.Sardar,
B.Davvaz,
S.Kayal,
S.K.Majumdar

**Abstract:**

**Keywords:**
Regular Γ-semigroup,
belong to or quasi-coincident,
(∈,
∈ ∨q)-fuzzy subsemigroup,
∈ ∨q)-fuzzy bi-ideals

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1072040

**References:**

[1] S.K. Bhakat and P. Das, (Ôêê,Ôêê Ôê¿q)-fuzzy subgroup, Fuzzy Sets Syst. 80 (1996) 359-368.

[2] S. Chattopadhyay, Right orthodox Γ-semigroup, Southeast Asian Bull. Math., 29 (2005) 23-30.

[3] R. Chinram, On quasi-Γ-ideals in Γ-semigroups, Science Asia 32 (2006) 351-353.

[4] T.K. Dutta and N.C. Adhikari, On Γ-semigroup with the right and left unities, Soochow J. Math., 19 (4) (1993) 461-474.

[5] T.K. Dutta and N.C. Adhikari, On prime radical of Γ-semigroup, Bull. Cal. Math. Soc., 86 (5) (1994) 437-444.

[6] T.K. Dutta, S.K. Sardar and S.K. Majumder, Fuzzy ideal extensions of Γ-semigroups via its operator semigroups, Int. J. Contemp. Math. Sciences, 4(30)(2009) 1455 - 1463.

[7] K. Hila, On some classes of le- Γ-semigroup and minimal quasi-ideals, Algebras Groups Geom. 24 (2007) 485-495.

[8] Y.B. Jun and S.Z. Song, Generalized fuzzy interior ideals in semigroups, Inform Sci. 176 (2006) 3079-3093.

[9] N. Kuroki, On fuzzy semigroups, Inform Sci. 53 (1991) 203-236.

[10] N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets Syst. 5 (1981) 203-215.

[11] N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets Syst. 158 (2004) 277-288.

[12] V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158(2004) 277-288.

[13] P.M. Pu and Y.M. Liu, Fuzzy topology I, neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980) 571-599.

[14] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971) 512-517.

[15] N.K. Saha, On Γ-semigroup II, Bull. Cal. Math. Soc. 79 (1987) 331-335.

[16] S.K. Sardar and S.K. Majumder, On fuzzy ideals in Γ-semigroups, International Journal of Algebra, 3 (16) (2009)775-784.

[17] S.K. Sardar, S.K. Majumder and D. Mandal, A note on characterization of prime ideals of Γ-semigroups in terms of fuzzy subsets,Int. J. Contemp. Math. Sciences, 4(30)(2009) 1465 -1472.

[18] S.K. Sardar and S.K. Majumder, A note on characterization of semiprime ideals of Γ-semigroups in terms of fuzzy subsets, International Journal of Pure and Applied Mathematics, 3(56)(2009)451-457.

[19] S.K. Sardar, B. Davvaz and S.K. Majumder, A study on fuzzy interior ideals of Γ-semigroups,Computers and Mathematics with applications(Elsevier),60 (2010) 90-94.

[20] S.K. Sardar, B. Davvaz, S.K. Majumder and S. Kayal, (╬▒, β)-fuzzy subsemigroup and (╬▒, β)-fuzzy bi-ideal in Γ- semigroups,(Communicated).

[21] M.K. Sen and S. Chattopadhyay, Semidirect product of a monoid and a Γ-semigroup, East-West J. Math. 6 (2004) 131-138.

[22] M.K. Sen and N.K. Saha, Orthodox Γ-semigroups, Internat. J. Math. Math. Sci., 13 (1990) 527-534.

[23] M.K. Sen and N.K. Saha, On Γ-semigroup I, Bull. Cal. Math. Soc. 78 (1986) 180-186.

[24] A. Seth, Γ-group congruences on regular Γ-semigroups, Internat. J. Math. Math. Sci. 15 (1992)103-106.

[25] Y. Yunqiang and D. Xu, The (Ôêê,Ôêê Ôê¿q)-fuzzy subsemigroups and ideals of an (Ôêê,Ôêê Ôê¿q)-fuzzy semigroup, Southeast Asian Bull. of math. 33 (2009)391-400.

[26] L.A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965) 338-353.