Intuitionistic fuzzy quasi-ideals in ordered semigroups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 67-81.

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In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semigroups with the help of intuitionistic fuzzy quasi-ideals.
Keywords: subsemigroups, quasi(bi)-ideals, left (right) regular, left (right) simple ordered semigroups, completely regular ordered semigroups, intuitionistic fuzzy sets, intuitionistic fuzzy subsemigroups, intuitionistic fuzzy quasi(bi)-ideals of ordered semigroups.
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A. Khan; M. Shabir; Y. B. Jun. Intuitionistic fuzzy quasi-ideals in ordered semigroups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 67-81. http://geodesic.mathdoc.fr/item/IVM_2010_12_a6/

[1] Steinfeld O., Quasi-ideals in rings and semigroups, Akademiakiado, Budapest, 1978 | MR | Zbl

[2] Kuroki N., “Fuzzy bi-ideals in semigroups”, Comment. Math. Univ., 28:1 (1979), 17–21 | MR | Zbl

[3] Kuroki N., “On fuzzy semigroups”, Fuzzy Sets Syst., 5 (1981), 203–215 | DOI | MR | Zbl

[4] Kuroki N., “Fuzzy semiprime quasi-ideals in semigroups”, Inf. Sci., 75:3 (1993), 201–211 | DOI | MR | Zbl

[5] Ahsan J., Latif R. M., Shabir M., “Fuzzy quasi-ideals of semigroups”, J. Fuzzy Math., 9:2 (2001), 259–270 | MR | Zbl

[6] Atanassov K. T., “Intuitionistic fuzzy sets”, Fuzzy Sets and Syst., 20:1 (1986), 87–96 | DOI | MR | Zbl

[7] Atanassov K. T., “New operations defined over the intuitionistic fuzzy sets”, Fuzzy Sets Syst., 61:2 (1994), 137–142 | DOI | MR | Zbl

[8] Atanassov K. T., Intuitionistic fuzzy sets. Theory and applications, Studies in Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg, 1999 | MR | Zbl

[9] Davvaz B., Dudek W. A., Jun Y. B., “Intuitionistic fuzzy $H_v$-submodules”, Inf. Sci., 176:3 (2006), 285–300 | DOI | MR | Zbl

[10] Kim K. H., Dudek W. A., Jun Y. B., “On intuitionistic fuzzy subquasigroups of a quasigroups”, Quasigroups Related Syst., 7:1 (2000), 15–28 | MR | Zbl

[11] Kim K. H., Jun Y. B., “Intuitionistic fuzzy ideals of semigroups”, Ind. J. Pure Appl. Math., 33:4 (2002), 443–449 | MR | Zbl

[12] Kim K. H., Jun Y. B., “Intuitionistic fuzzy interior ideals of semigroups”, Int. J. Math. Sci., 27:5 (2001), 261–267 | DOI | MR | Zbl

[13] Jun Y. B., Öztürk M. A., Park C. H., “Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings”, Inf. Sci., 177:21 (2007), 4662–4677 | DOI | MR | Zbl

[14] Kehayopulu N., Tsingelis M., “Regular ordered semigroups in terms of fuzzy subsets”, Inf. Sci., 176:24 (2006), 3675–3693 | DOI | MR | Zbl

[15] Kehayopulu N., Tsingelis M., “Fuzzy sets in ordered groupoids”, Semigroup Forum, 65:1 (2002), 128–132 | DOI | MR | Zbl

[16] Kehayopulu N., Tsingelis M., “Fuzzy bi-ideals in ordered semigroups”, Inf. Sci., 171:1–3 (2005), 13–28 | DOI | MR | Zbl

[17] Kehayopulu N., “On left regular ordered semigroups”, Math. Japon., 35:6 (1990), 1057–1060 | MR | Zbl

[18] Kehayopulu N., “On regular duo ordered semigroups”, Math. Japon., 37:3 (1992), 535–540 | MR | Zbl

[19] Kehayopulu N., “On completely regular ordered semigroups”, Sci. Math., 1:1 (1998), 27–32 | MR | Zbl

[20] Kehayopulu N., “Remarks on ordered semigroups”, Pure Math. Appl., 7:1–2 (1990), 111–128 | MR

[21] Shabir M., Khan A., “Characterizations of ordered semigroups by the properties of their intuitionistic fuzzy generalized bi-ideals”, J. Fuzzy Syst. Math., 23:5 (2009), 110–119 | MR

[22] Shabir M., Khan A., “Characterizations of ordered semigroups by the properties of their fuzzy ideals”, Comput. Math. Appl., 59:1 (2010), 539–549 | DOI | MR | Zbl

[23] Kehayopulu N., Tsingelis M., “On the decomposition of prime ideals of ordered semigroups into their $\mathcal N$-classes”, Semigroup Forum, 47:3 (1993), 393–395 | DOI | MR | Zbl