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Characterizations of \(h\)-intra- and \(h\)-quasi-hemiregular hemirings. (English) Zbl 1247.16048

Summary: The concepts of \((\in_\gamma,\in_\gamma\!\vee\,q_\delta)\)-fuzzy \(h\)-bi-(\(h\)-quasi-)ideals of hemirings are introduced. Some new characterization theorems of these kinds of fuzzy \(h\)-ideals are also given. In particular, some characterizations of the \(h\)-intra-hemiregular and \(h\)-quasi-hemiregular hemirings are investigated by these kinds of fuzzy \(h\)-ideals.

MSC:

16Y99 Generalizations
16D25 Ideals in associative algebras
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[1] Glazek, K., A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences: With Complete Bibliography (2002), Kluwer Acad. Publ: Kluwer Acad. Publ Dodrecht · Zbl 1072.16040
[2] Jonathan, S.; Golan, J. S., Semirings and their Applications (1999), Kluwer: Kluwer Dodrecht · Zbl 0947.16034
[3] Wechler, W., The Concept of Fuzziness in Automata and Language Theory (1978), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0401.94048
[4] Henriksen, M., Ideals in semirings with commutative addition, Amer. Math. Soc. Notices, 6, 321 (1958)
[5] Jun, Y. B.; Kim, H. S.; Öztürk, M. A., Fuzzy \(k\)-ideals in semirings, J. Fuzzy Math., 13, 351-364 (2005) · Zbl 1083.16026
[6] Jun, Y. B.; Öztürk, M. A.; Song, S. Z., On fuzzy \(h\)-ideals in hemirings, Inform. Sci., 162, 211-226 (2004) · Zbl 1064.16051
[7] Zhan, J.; Dudek, W. A., Fuzzy \(h\)-ideals of hemirings, Inform. Sci., 177, 876-886 (2007) · Zbl 1118.16031
[8] Yin, Y.; Li, H., The characterization of \(h\)-hemiregular hemirings and \(h\)-intra-hemiregular hemirings, Inform. Sci., 178, 3451-3464 (2008) · Zbl 1152.16038
[9] Ma, X.; Zhan, J., Generalized fuzzy \(h\)-bi-ideals and \(h\)-quasi-ideals of hemirings, Inform. Sci., 179, 1249-1268 (2009) · Zbl 1166.16024
[10] Akram, M., Bifuzzy left \(h\)-ideals of hemirings with interval-valued membership function, Math. Slovaca, 59, 6, 719-730 (2009) · Zbl 1202.16039
[11] Akram, M.; Dudek, W. A., Intuitionistic fuzzy left \(k\)-ideals of semirings, Soft Comput., 12, 5, 881-890 (2008) · Zbl 1151.16043
[12] Dudek, W. A., Special types of intuitionistic fuzzy left \(h\)-ideals of hemirings, Soft Comput., 12, 359-364 (2008) · Zbl 1137.16041
[13] Dudek, W. A., Intuitionistic fuzzy \(h\)-ideals of hemirings, WSEAS Trans. Math., 12, 1315-1331 (2006)
[14] Dudek, W. A.; Shabir, M.; Irfan Ali, M., \((\alpha, \beta)\)-fuzzy ideals of hemirings, Comput. Math. Appl., 58, 310-321 (2009) · Zbl 1189.16041
[15] Dudek, W. A.; Shabir, M.; Anjum, R., Characterizations of hemirings by their \(h\)-ideals, Comput. Math. Appl., 59, 3167-3179 (2010) · Zbl 1217.16042
[16] Dutta, T. K.; Biswas, B. K., Fuzzy prime ideals of a semiring, Bull. Malays. Math. Sci. Soc., 17, 9-16 (1994) · Zbl 0848.16038
[17] Dutta, T. K.; Biswas, B. K., Fuzzy \(k\)-ideals of semirings, Bull. Malays. Math. Sci. Soc., 30, 1, 65-73 (2005) · Zbl 1141.16039
[18] Feng, F.; Jun, Y. B.; Zhao, X. Z., On \({}^\ast - \lambda \)-semirings, Inform. Sci., 177, 5012-5023 (2007) · Zbl 1142.16032
[19] Feng, F.; Zhao, X. Z.; Jun, Y. B., On \({}^\ast - \mu \)-semirings and \(\ast - \lambda \)-semirings, Theoret. Comput. Sci., 347, 423-431 (2005) · Zbl 1080.68067
[20] Jun, Y. B., Note on \((\alpha, \beta)\)-fuzzy ideals of hemirings, Comput. Math. Appl., 59, 2582-2586 (2010) · Zbl 1193.16040
[21] La Torre, D. R., On \(h\)-ideals and \(k\)-ideals in hemirings, Publ. Math. Debrecen, 12, 219-226 (1965) · Zbl 0168.28302
[22] Ma, X.; Zhan, J., Fuzzy \(h\)-ideals in \(h\)-hemiregular and \(h\)-semisimple \(\Gamma \)-hemirings, Neural Comput. Appl., 19, 477-485 (2010)
[23] Yin, Y.; Huang, X.; Xu, D.; Li, H., The characterization of \(h\)-semisimple hemirings, Int. J. Fuzzy Systems, 11, 116-122 (2009)
[24] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606
[25] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci., 172, 1-40 (2005) · Zbl 1074.94021
[26] Bhakat, S. K.; Das, P., Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81, 383-393 (1996) · Zbl 0878.16025
[27] Davvaz, B., \((\in, \in \vee q)\)-fuzzy subnear-rings and ideals, Soft Comput., 10, 206-211 (2006) · Zbl 1084.16040
[28] Ma, X.; Zhan, J., On fuzzy \(h\)-ideals of hemirings, J. Syst. Sci. Complexity, 20, 470-478 (2007) · Zbl 1333.16046
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