Bijan Davvaz


In this paper, we introduce the concept of generalized
fuzzy ideals in ternary semigroups, which is a generalization of the fuzzy
ideals of semigroups. In this regard, we define ($\alpha ,\beta $)-fuzzy
left (right, lateral) ideals, ($\alpha ,\beta $)-fuzzy quasi-ideals and ($
\alpha ,\beta $)-fuzzy bi-ideals and invetigate some related properties of
ternary semigroups. Special concentration is paid to ($\in ,\in \vee q$
)-fuzzy left (right, lateral) ideals, ($\in ,\in \vee q$)-fuzzy quasi-ideals
and ($\in ,\in \vee q$)-fuzzy bi-ideals. Finally, we
characterize regular ternary semigroups in terms of these notions.

DOI : http://dx.doi.org/10.22342/jims.


Fuzzy subset; ($\in ,\in \vee q$)-fuzzy left (right,

Full Text:



bibitem{1} J. Ahsan, Kui Yuan Li, M. Shabir, textit{Semigroups

characterized by their fuzzy bi-ideals}, J. Fuzzy Math., 10(2) (2002) 441-449.

bibitem{2} S. K. Bhakat, $left( in vee qright) $-textit{level subset},

Fuzzy Sets Syst., 103 (1999) 529-533.

bibitem{3} S. K. Bhakat, P. Das, textit{On the definition of a fuzzy

subgroup}, Fuzzy Sets Syst., 51 (1992) 235-241.

bibitem{4} S. K. Bhakat, P. Das, $left( in ,in vee qright) $-textit{%

fuzzy subgroups}, Fuzzy Sets Syst., 80 (1996) 359-368.

bibitem{5} S. K. Bhakat, P. Das, textit{Fuzzy subrings and ideals redefined}, Fuzzy Sets Syst., 81 (1996) 383-393.

bibitem{6} P. S. Das, textit{Fuzzy groups and level subgroups}, J. Math.

Anal. Appl., 84 (1981) 264-269.

bibitem{7} B. Davvaz, $left( in ,in vee qright) $-textit{fuzzy

subnearrings and ideals}, Soft Computing, 10 (2006) 206-211.

bibitem{d} B. Davvaz, {it Fuzzy $R$-subgroups with thresholds of near-rings and implication operators}, Soft

Computing, 12 (2008) 875-879.

bibitem{8} V. N. Dixit, S. Dewan, textit{A note on quasi and

bi-ideals in Ternary Semigroups}, Internat. J. Math. Math. Sci., 18(3) (1995) 501-508.

bibitem{9} T. K. Dutta, S. Kar, textit{On ternary semifields,} Math.

Gen. Algebra Appl., 24 (2004) 445-454.

bibitem{10} T. K. Dutta, S. Kar, textit{On Prime ideals and Prime Radical

of Ternary Semirings,} Bull. Cal. Math. Soc., 97(5)(2005) 185-198.

bibitem{11} T. K. Dutta, S. Kar, textit{A note on regular ternary

semirings}, Kyungpook Math. J., 46 (2006) 357-365.

bibitem{12} A. Iampan, textit{The Minimality and Maximality of Left

(Right) Ideals in Ternary Semigroups}, Int. J. Contem. Math. Sci., 5 (2010) 2409-2417.

bibitem{13} Y. B. Jun, S. Z. Song, textit{Generalized fuzzy interior ideals

in semigroups}, Information Sciences, 176 (2006) 3079-3093.

bibitem{14} Y. B. Jun, textit{Generalization of }$(in ,in vee q)$textit{%

-fuzzy sub algebras in BCK/BCI-algebras,} Comput. Math. Appl. 58 (2009)


bibitem{15} Y. B. Jun, Y. Xu, J. Ma, textit{Redefined fuzzy implicative

filters}, Information Sciences, 177 (2007) 1422-1429..

bibitem{16} O. Kazanci, S. Yamak, textit{Generalized fuzzy bi-ideals of

semigroup}, Soft Computing, 12 (2008) 1119-1124.

bibitem{17} S.Kar, textit{On Ideals in ternary semirings}, Int.J. Math.

Gen. Sci., 18 (2005) 3015-3023.

bibitem{18} A. Khan, Y. B. Jun, M. Z. Abbas, textit{Characterizations of

ordered semigroups in terms of (}$in ,in vee q$textit{)-fuzzy interior

ideals}, Neural Computing and Applications, DOI 10.1007/s00521-010-0463-8.

bibitem{19} N. Kuroki, textit{Fuzzy bi-ideals in semigroups}, Comment. Math.

Univ. St. Pauli XXVIII-1 (1979) 17-21.

bibitem{20} D. H. Lehmer, textit{A ternary analogue of abelian groups},

Amer. J. Math., (1932) 329-338.

bibitem{21} J. N. Mordeson, D. S. Malik and N. Kuroki, textit{Fuzzy

Semigroups}, Studies in Fuzziness and Soft Computing, 131,

Springer-Verlag Berlin (2003).

bibitem{22} V. Murali, textit{Fuzzy points of equivalent fuzzy subsets,}

Information Sciences, 158 (2004) 277-288.

bibitem{24} M. Shabir, Y. B. Jun and Y. Nawaz,textit{ Semigroups characterized

by }$(in ,in vee q)$textit{-fuzzy ideals,} Comput. Math. Appl., 60 (2010) 1473-1493.

bibitem{25} M. Shabir, Y. B. Jun, Y. Nawaz, textit{Characterizations of

regular semigroups by (}$alpha ,beta $textit{)-fuzzy ideals}, Comput.

Math. Appli., 59 (2010) 161-175.

bibitem{26} F. M. Sioson, textit{Ideal theory in ternary semigroups},

Math.Japon., 10 (1965) 63-84.

bibitem{27} L. A. Zadeh, textit{Fuzzy Sets}, Inform. & Control, 8 (1965)


bibitem{28} J. Zhan, B. Davvaz, K. P. Shum, textit{A new view of fuzzy

hypernear-rings}, Information Sciences, 178 (2008) 425-438.

DOI: https://doi.org/10.22342/jims.


  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243
Email: jims.indoms@gmail.com

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats