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BIPOLAR FUZZY HYPER BCK-IDEALS IN HYPER BCK-ALGEBRAS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 8، شماره 2، شهریور 2011، صفحه 105-120 اصل مقاله (185.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2011.279 | ||
| نویسندگان | ||
| Young Bae Jun1؛ Min Su Kang* 2؛ Hee Sik Kim2 | ||
| 1Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Korea | ||
| 2Department of Mathematics, Hanyang University, Seoul 133-791, Korea | ||
| چکیده | ||
| Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, 𝑠-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed. Moreover, several related properties are investigated. | ||
| کلیدواژه‌ها | ||
| (Strong؛ weak؛ s-weak) hyper BCK-ideal؛ Bipolar fuzzy hyper BCKideal؛ Bipolar fuzzy strong hyper BCK-ideal؛ Bipolar fuzzy weak hyper BCK-ideal؛ Bipolar fuzzy s-weak hyper BCK-ideal؛ inf-sup property | ||
| مراجع | ||
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[1] B. Davvaz, Fuzzy hyperideals in ternary semihyperrings, Iranian Journal of Fuzzy Systems, 6(4) (2009), 21-36. [2] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press, 1980. [3] H. Harizavi, Prime weak hyper BCK-ideals of lower hyper BCK-semilattice, Sci. Math. Jpn., 68 (2008), 353-360. [4] Y. B. Jun and W. H. Shim, Fuzzy implicative hyper 𝐵𝐶𝐾-ideals of hyper 𝐵𝐶𝐾-algebras, Internat. J. Math. Math. Sci., 29(2) (2002), 63-70. [5] Y. B. Jun and X. L. Xin, Scalar elements and hyperatoms of hyper 𝐵𝐶𝐾-algebras, Scientiae Mathematicae, 2(3) (1999), 303-309. [6] Y. B. Jun and X. L. Xin, Fuzzy hyper 𝐵𝐶𝐾-ideals of hyper 𝐵𝐶𝐾-algebras, Sci. Math. Jpn., 53(2) (2001), 353-360. [7] Y. B. Jun, X. L. Xin, E. H. Roh and M. M. Zahedi, Strong hyper 𝐵𝐶𝐾-ideals of hyper 𝐵𝐶𝐾-algebras, Math. Japonica, 51(3) (2000), 493-498. [8] Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei, On hyper 𝐵𝐶𝐾-algebras, Italian J. of Pure and Appl. Math., 8 (2000), 127-136. [9] K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000), 307-312. [10] K. M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolarvalued fuzzy sets, J. Fuzzy Logic Intelligent Systems, 14(2) (2004), 125-129. [11] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm, (1934), 45-49. [12] L. Torkzadeh, M. Abbasi and M. M. Zahedi, Some results of intuitionistic fuzzy weak dual hyper K-ideals, Iranian Journal of Fuzzy Systems, 5(1) (2008), 65-78. [13] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. [14] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer-Nijhoff Publishing, 1985. | ||
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