Abstract
In this paper we apply the concept of interval-valued bifuzzy sets to hemirings. We introduce the notion of interval-valued bifuzzy left h-ideals of hemirings and investigate some of their properties. Using interval-valued bifuzzy left h-ideals, characterizations of Artinian and Noetherian hemirings are established.
[1] AHO, A. W. ULLMAN, J. D.: Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979. Search in Google Scholar
[2] AKRAM, M. DAR, K. H.: On anti fuzzy left h-ideals in hemirings, Internat. Math. Forum 2 (2007), 2295–2304. 10.12988/imf.2007.07204Search in Google Scholar
[3] AKRAM, M. DAR, K. H.: Fuzzy left h-ideals in hemirings with respect to a s-norm, Internat. J. Comput. Appl. Math. 2 (2007), 7–14. Search in Google Scholar
[4] AKRAM, M. DUDEK, W. A.: Intuitionistic fuzzy left k-ideals of semirings, Soft Comput. 12 (2008), 881–890. http://dx.doi.org/10.1007/s00500-007-0256-x10.1007/s00500-007-0256-xSearch in Google Scholar
[5] ATANASSOV, K. T.: Intuitionistic fuzzy sets. VII ITKRs Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), 1983 (Bulgarian). Search in Google Scholar
[6] ATANASSOV, K. T.: Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96. http://dx.doi.org/10.1016/S0165-0114(86)80034-310.1016/S0165-0114(86)80034-3Search in Google Scholar
[7] ATANASSOV, K. T. GARGOV, G.: Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), 343–349. http://dx.doi.org/10.1016/0165-0114(89)90205-410.1016/0165-0114(89)90205-4Search in Google Scholar
[8] ATANASSOV, K. T.: Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 64 (1994), 159–174. http://dx.doi.org/10.1016/0165-0114(94)90331-X10.1016/0165-0114(94)90331-XSearch in Google Scholar
[9] DUDEK, W. A.: Intuitionistic fuzzy h-ideals of hemirings, WSEAS Trans. Math. 12 (2006), 1315–1321. Search in Google Scholar
[10] GOLAN, J. S.: Semirings and their applications, Kluwer Academic Publishers, Dordrecht, 1999. 10.1007/978-94-015-9333-5Search in Google Scholar
[11] IZUKA, K.: On the Jacobson radical of a semiring, Tohoku Math. J. (2) 11 (1959), 409–421. http://dx.doi.org/10.2748/tmj/117824453810.2748/tmj/1178244538Search in Google Scholar
[12] JUN, Y. B. ÖZTÜRK, M. A. SONG, S. Z.: On h-fuzzy ideals in hemirings, Inform. Sci. 162 (2004), 211–226. http://dx.doi.org/10.1016/j.ins.2003.09.00710.1016/j.ins.2003.09.007Search in Google Scholar
[13] HENRIKSEN, M.: Ideals in semirings with commutative addition, Notices Amer. Math. Soc. 6 (1958), 321. Search in Google Scholar
[14] KIM, C. B. PARK, M.: k-fuzzy ideals in semirings, Fuzzy Sets and Systems 81 (1996), 281–286. http://dx.doi.org/10.1016/0165-0114(95)00161-110.1016/0165-0114(95)00161-1Search in Google Scholar
[15] LA TORRE, D. R.: On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12 (1965), 219–226. Search in Google Scholar
[16] OLSON, D. M.: A note on the homomorphism theorem for hemirings, Int. J. Math. Math. Sci. 1 (1978), 439–445. http://dx.doi.org/10.1155/S016117127800044710.1155/S0161171278000447Search in Google Scholar
[17] GERSTENKORN, T. MAŃKO, J.: Bifuzzy probabilistic sets, Fuzzy Sets and Systems 71 (1995), 207–214. http://dx.doi.org/10.1016/0165-0114(94)00254-510.1016/0165-0114(94)00254-5Search in Google Scholar
[18] WANG, H.: On rational series and rational languages, Theoret. Comput. Sci. 205 (1998), 329–336. http://dx.doi.org/10.1016/S0304-3975(98)00103-010.1016/S0304-3975(98)00103-0Search in Google Scholar
[19] ZADEH, L. A.: Fuzzy sets, Inform. and Control (Shenyang) 8 (1965), 338–353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X10.1016/S0019-9958(65)90241-XSearch in Google Scholar
[20] ZADEH, L. A.: The concept of a lingusistic variable and its application to approximate reasoning, Inform. Sci. 8 (1975), 199–249. http://dx.doi.org/10.1016/0020-0255(75)90036-510.1016/0020-0255(75)90036-5Search in Google Scholar
[21] ZHAN, J. DUDEK, W. A.: Fuzzy h-ideals of hemirings, Inform. Sci. 177 (2007), 876–886. http://dx.doi.org/10.1016/j.ins.2006.04.00510.1016/j.ins.2006.04.005Search in Google Scholar
© 2009 Mathematical Institute, Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.