Characterizations of -fuzzy fantastic ideals in BCI-algebras

Authors

  • MUHAMMAD ZULFIQAR Department of Mathematics, GC University Lahore, Pakistan

Keywords:

BCI-algebra, fuzzy fantastic ideal, -fuzzy fantastic ideals, fuzzy fantastic ideal with thresholds.

Abstract

In this paper, the concepts of  -fuzzy fantastic ideals and  -fuzzy fantastic ideals in BCI-algebras are introduced and investigate some of their properties. The concept of a fuzzy fantastic ideal with thresholds, properties of a fuzzy fantastic ideal, an  -fuzzy fantastic ideal and an  -fuzzy fantastic ideal are discussed.

References

Bhakat, S. K. 1999. ( )-level subsets. Fuzzy Sets and Systems 103: 529-533.

Bhakat, S. K. 2000. -fuzzy normal, quasinormal and maximal subgroups. Fuzzy Sets and Systems 112: 299-312.

Das, P. S. 1981. Fuzzy groups and level subgroups. Journal of Mathematical Analysis and Applications 84: 264-269.

Bhakat, S. K. Das, P. 1996. -fuzzy subgroups. Fuzzy Sets and Systems 80: 359-368.

Guangji, Z., Cheng, Z., Zixin, L. Jiatai, G. 2006. New kinds of fuzzy ideals in BCI-algebras. Fuzzy Optimization and Decision Making 5: 177-186.

Huang, Y. S. 2006. BCI-algebras. Science Press, China.

Jun, Y. B. 2004. On ( , )-fuzzy ideals of BCK/BCI-algebras. Scientiae Mathematicae Japonicae 60: 613-617.

Jun, Y. B. 2005. On ( , )-fuzzy subalgebras of BCK/BCI-algebras. Bulletin of the Korean Mathematical Society 42: 703-711.

Jun, Y. B. 2007. Fuzzy subalgebras of type ( , ) in BCK/BCI-algebras. Kyungpook Mathematical Journal 47: 403-410.

Jun, Y. B. 2009. Generalizations of -fuzzy subalgebras in BCK/BCI-algebras. Computers and Mathematics with Applications 58: 1383-1390.

Jun, Y. B., Lee, K. J. Park, C. H. 2010. New types of fuzzy ideals in BCK/BCI- algebras. Computers and Mathematics with Applications 60: 771-785.

Ma, X., Zhan, J., Davvaz, B. Jun, Y. B. 2008. Some kinds of -interval- valued fuzzy ideals of BCI-algebras. Information Sciences 178: 3738-3754.

Meng, J. 1997. On ideals in BCK-algebras. Mathematica Japonica 40: 143-154.

Meng, J. Guo, X. 2005. On fuzzy ideals in BCK/ BCI-algebras. Fuzzy sets and Systems 149: 509-525.

Meng, J. Jun, Y. B. 1994. BCK-algebras. Kyung Moon Sa Co., Seoul, Korea.

Meng, J., Jun, Y. B. Kim, H. S. 1997. Fuzzy implicative ideals of BCK-algebras. Fuzzy sets and Systems 89: 243-248.

Murali, V. 2004. Fuzzy points of equivalent fuzzy subsets. Information Sciences 158: 277-288.

Pu, P. M. Liu, Y. M. 1980. Fuzzy topology I: neighourhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Applications 76: 571-599.

Rosenfeld, A. 1971. Fuzzy groups. Journal of Mathematical Analysis and Applications 35: 512-517.

Saeid, A. B. 2010. Fantastic ideals in BCI-algebras. World Applied Sciences Journal 8 (5): 550-554.

Xi, O. G. 1991. Fuzzy BCK-algebras. Mathematica Japonica 36: 935-942.

Ying, M. S. 1991. A1991. A new approach for fuzzy topology (I). Fuzzy Sets and Systems 39: 303-321.

Ying, M. S. 1988. On standard models of fuzzy modal logics. Fuzzy Sets and Systems 26: 357-363.

Yuan, X., Zhang, C. Ren, Y. 2003. Generalized fuzzy groups and many-valued implications. Fuzzy Sets and Systems 138: 205-211.

Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8: 338-353.

Zhan, J. Jun, Y. B. 2009. Generalized fuzzy ideals of BCI-algebras. Bulletin of the Malaysian Mathematical Sciences Society 32: 119-130.

Zhan, J. Jun, Y. B. 2011. On -fuzzy ideals of BCI-algebras. Neural Computing and Applications 20: 319-328.

Zhan, J., Jun, Y. B. Davvaz, B. 2009. On -fuzzy ideals of BCI-algebras. Iranian Journal of Fuzzy Systems 6 (1): 81-94.

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Published

07-01-2014