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Soft Lattice Implication Algebras Based on Fuzzy Sets

Year 2011, Volume: 40 Issue: 4, 483 - 492, 01.04.2011

Abstract

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈ ∨q)- fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

References

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  • Bhakat, S. K. and Das, P. (∈, ∈ ∨ q)-fuzzy subgroup, Fuzzy Sets and Systems 80, 359–368, Jun, Y. B. Soft BCK/BCI-algebras, Comput. Math. Appl. 56, 1408–1413, 2008.
  • Jun, Y. B. and Park, C. H. Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466–2475, 2008.
  • Jun, Y. B., Xu, Y. and Ma, J. Redefined fuzzy implicative filters, Inform. Sci. 177, 1422– , 2007.
  • Jun, Y. B., Xu, Y. and Qin, K. Fuzzy filters redefined in lattice implication algebras, J. Fuzzy Math. 14, 345–353, 2006.
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  • Pu, P. M. and Liu, Y. M. Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980.
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  • Xu, Y. and Qin, K. Y. On fuzzy filters of lattice implication algebras, J. Fuzzy Math. 1, –260, 1993.
  • Xu, Y., Ruan, D., Qin, K. and Liu, J. Lattice-valued Logic (Springer, Berlin, 2003).
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  • Zadeh, L. A. Toward a generalized theory of uncertainty (GTU)-an outine, Inform. Sci. 172, –40, 2005.
  • Zhan, J., Chen, Y. and Tan, Z. Fuzzy fantastic filters of lattice implication algebras, Sci. Math. Japon 59, 159–161, 2004.
  • Zhan, J. and Jun, Y. B. Notes on redefined fuzzy implicative filters of lattice implication algebras, Inform. Sci. 179, 3182–3186, 2009.
  • Zhan, J. and Tan, Z. On n-fold fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math. 14, 103–123, 2006.
  • Zhan, J. and Xu, Y. Generalized fuzzy filters of lattice implication algebras, FSKD, IEEE Computer Society 6, 281–283, 2009.

Soft Lattice Implication Algebras Based on Fuzzy Sets

Year 2011, Volume: 40 Issue: 4, 483 - 492, 01.04.2011

Abstract

References

  • Aktas, H. and Cagman, N. Soft sets and soft groups, Inform. Sci. 177, 2726–2735, 2007.
  • Bhakat, S. K. and Das, P. (∈, ∈ ∨ q)-fuzzy subgroup, Fuzzy Sets and Systems 80, 359–368, Jun, Y. B. Soft BCK/BCI-algebras, Comput. Math. Appl. 56, 1408–1413, 2008.
  • Jun, Y. B. and Park, C. H. Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466–2475, 2008.
  • Jun, Y. B., Xu, Y. and Ma, J. Redefined fuzzy implicative filters, Inform. Sci. 177, 1422– , 2007.
  • Jun, Y. B., Xu, Y. and Qin, K. Fuzzy filters redefined in lattice implication algebras, J. Fuzzy Math. 14, 345–353, 2006.
  • Maji, P. J., Roy, A. R. and Biswas, R. An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002.
  • Maji, P. K., Biswas, R. and Roy, A. R. Soft set theory, Comput. Math. Appl. 45, 555–562, Molodtsov, D. Soft set theory - First results, Comput. Math. Appl. 37, 19–31, 1999.
  • Pu, P. M. and Liu, Y. M. Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980.
  • Xu, Y. Lattice implication algebras, J. Southeast Jiaotong Univ. (in Chinese) 1, 20–27, 1993.
  • Xu, Y. and Qin, K. Y. On fuzzy filters of lattice implication algebras, J. Fuzzy Math. 1, –260, 1993.
  • Xu, Y., Ruan, D., Qin, K. and Liu, J. Lattice-valued Logic (Springer, Berlin, 2003).
  • Zadeh, L. A. From circuit theory to system theory, Proc. Inst. Radio Eng. 50, 856–865, 1962.
  • Zadeh, L. A. Toward a generalized theory of uncertainty (GTU)-an outine, Inform. Sci. 172, –40, 2005.
  • Zhan, J., Chen, Y. and Tan, Z. Fuzzy fantastic filters of lattice implication algebras, Sci. Math. Japon 59, 159–161, 2004.
  • Zhan, J. and Jun, Y. B. Notes on redefined fuzzy implicative filters of lattice implication algebras, Inform. Sci. 179, 3182–3186, 2009.
  • Zhan, J. and Tan, Z. On n-fold fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math. 14, 103–123, 2006.
  • Zhan, J. and Xu, Y. Generalized fuzzy filters of lattice implication algebras, FSKD, IEEE Computer Society 6, 281–283, 2009.
There are 17 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Jianming Zhan This is me

Yang Xu This is me

Publication Date April 1, 2011
Published in Issue Year 2011 Volume: 40 Issue: 4

Cite

APA Zhan, J., & Xu, Y. (2011). Soft Lattice Implication Algebras Based on Fuzzy Sets. Hacettepe Journal of Mathematics and Statistics, 40(4), 483-492.
AMA Zhan J, Xu Y. Soft Lattice Implication Algebras Based on Fuzzy Sets. Hacettepe Journal of Mathematics and Statistics. April 2011;40(4):483-492.
Chicago Zhan, Jianming, and Yang Xu. “Soft Lattice Implication Algebras Based on Fuzzy Sets”. Hacettepe Journal of Mathematics and Statistics 40, no. 4 (April 2011): 483-92.
EndNote Zhan J, Xu Y (April 1, 2011) Soft Lattice Implication Algebras Based on Fuzzy Sets. Hacettepe Journal of Mathematics and Statistics 40 4 483–492.
IEEE J. Zhan and Y. Xu, “Soft Lattice Implication Algebras Based on Fuzzy Sets”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, pp. 483–492, 2011.
ISNAD Zhan, Jianming - Xu, Yang. “Soft Lattice Implication Algebras Based on Fuzzy Sets”. Hacettepe Journal of Mathematics and Statistics 40/4 (April 2011), 483-492.
JAMA Zhan J, Xu Y. Soft Lattice Implication Algebras Based on Fuzzy Sets. Hacettepe Journal of Mathematics and Statistics. 2011;40:483–492.
MLA Zhan, Jianming and Yang Xu. “Soft Lattice Implication Algebras Based on Fuzzy Sets”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, 2011, pp. 483-92.
Vancouver Zhan J, Xu Y. Soft Lattice Implication Algebras Based on Fuzzy Sets. Hacettepe Journal of Mathematics and Statistics. 2011;40(4):483-92.