Research Article
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Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras

Year 2019, Volume: 32 Issue: 2, 649 - 658, 01.06.2019
https://izlik.org/JA97JB45ZY

Abstract

In
this study, the intuitionistic fuzzy congruence relations on intuitionistic
fuzzy abstract algebras were examined using Zadeh extension principle. Some
basic properties of intuitionistic fuzzy congruence relations on n-ary
operations were obtained.

References

  • [1] Atanassov K.T., Intuitionistic Fuzzy Sets, VII ITKR.s Session, SoÖa, June 1983.
  • [2] K. T. Atanassov, Studies in fuzziness and soft computing-on intuitionistic fuzzy sets theory, ISBN 978-3-642-29126-5, Springer 2012.
  • [3] Birkho§ G., LatticeTheory, American Mathematical Society, United States of America, 418 p., (1940).
  • [4] Burillo P., Bustince H., Intuitionistic fuzzy relations (Part I) Mathware Soft Comput., 2 (1995), 5-38.
  • [5] Bustince H., Burillo P., Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78 (1996), 293-303.
  • [6] Cohn P.M., Universal Algebra, D. Reidel Publishing Company, Dordrecht: Holland/ Boston: U.S.A/ London: England, 412 p., (1981).
  • [7] Çuvalcıoglu, G.; Yılmaz, S. Some properties of intuitionistic Fuzzy equivalence relations º and class trees w.r.t. intuitionistic Fuzzy equivalence relations. ADV. STUDIES CONTEMP. · MATH, 2014, 1(24), 1-9.
  • [8] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Universal Algebra in Intuitionistic Fuzzy Set Theory, º Notes on Intuitionistic Fuzzy Sets, 23 (1), 2017, 1-5.
  • [9] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Isomorphism theorems on Intuitionistic Fuzzy Universal º Algebras, Hacettepe Journal of Mathematics and Statistics, under review.
  • [10] Deschrijver G., Kerre E.E., On the composition of intuitionistic fuzzy relations, Fuzzy Sets and systems, 2003, 136, 333ñ361.
  • [11] Hur K, Su Y. J., Hee W. K., The lattice of intuitionistic fuzzy congruences, Int. Math. Forum, 5(1), 2006, 211-236.
  • [12] Hur K., Jang S. Y. and Ahn Y. S., Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2), 2005, 163-181.
  • [13] Li M., Cut sets of intuitionistic fuzzy sets (in Chinese), Journal of Liaoning Normal university, 30(2) (2007) 152-154.
  • [14] Mural¨V., A Study of Universal Algebra in Fuzzy Set Theory, Rhodes University, Department of Mathematics, PhD. Thesis, 1987, 104p.
  • [15] Mural¨V., Fuzzy congruence relations, Fuzzy Sets and Systems, 41(3), 1991, 359-369.
  • [16] Palaniappan N., Naganathan S. and Arjunan K., A study on Intuitionistic L-Fuzzy Subgroups, App. Math. Sciences, 3(53), 2009, 2619-2624.
  • [17] Zadeh L.A., Fuzzy Sets, Information and Control, 8, 1965, 338-353.
  • [18] Zadeh L.A., The concept of linguistic variable and its application to approximate reasoning. Inform. Sci., 8 (1975). 133-139.

Year 2019, Volume: 32 Issue: 2, 649 - 658, 01.06.2019
https://izlik.org/JA97JB45ZY

Abstract

References

  • [1] Atanassov K.T., Intuitionistic Fuzzy Sets, VII ITKR.s Session, SoÖa, June 1983.
  • [2] K. T. Atanassov, Studies in fuzziness and soft computing-on intuitionistic fuzzy sets theory, ISBN 978-3-642-29126-5, Springer 2012.
  • [3] Birkho§ G., LatticeTheory, American Mathematical Society, United States of America, 418 p., (1940).
  • [4] Burillo P., Bustince H., Intuitionistic fuzzy relations (Part I) Mathware Soft Comput., 2 (1995), 5-38.
  • [5] Bustince H., Burillo P., Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78 (1996), 293-303.
  • [6] Cohn P.M., Universal Algebra, D. Reidel Publishing Company, Dordrecht: Holland/ Boston: U.S.A/ London: England, 412 p., (1981).
  • [7] Çuvalcıoglu, G.; Yılmaz, S. Some properties of intuitionistic Fuzzy equivalence relations º and class trees w.r.t. intuitionistic Fuzzy equivalence relations. ADV. STUDIES CONTEMP. · MATH, 2014, 1(24), 1-9.
  • [8] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Universal Algebra in Intuitionistic Fuzzy Set Theory, º Notes on Intuitionistic Fuzzy Sets, 23 (1), 2017, 1-5.
  • [9] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Isomorphism theorems on Intuitionistic Fuzzy Universal º Algebras, Hacettepe Journal of Mathematics and Statistics, under review.
  • [10] Deschrijver G., Kerre E.E., On the composition of intuitionistic fuzzy relations, Fuzzy Sets and systems, 2003, 136, 333ñ361.
  • [11] Hur K, Su Y. J., Hee W. K., The lattice of intuitionistic fuzzy congruences, Int. Math. Forum, 5(1), 2006, 211-236.
  • [12] Hur K., Jang S. Y. and Ahn Y. S., Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2), 2005, 163-181.
  • [13] Li M., Cut sets of intuitionistic fuzzy sets (in Chinese), Journal of Liaoning Normal university, 30(2) (2007) 152-154.
  • [14] Mural¨V., A Study of Universal Algebra in Fuzzy Set Theory, Rhodes University, Department of Mathematics, PhD. Thesis, 1987, 104p.
  • [15] Mural¨V., Fuzzy congruence relations, Fuzzy Sets and Systems, 41(3), 1991, 359-369.
  • [16] Palaniappan N., Naganathan S. and Arjunan K., A study on Intuitionistic L-Fuzzy Subgroups, App. Math. Sciences, 3(53), 2009, 2619-2624.
  • [17] Zadeh L.A., Fuzzy Sets, Information and Control, 8, 1965, 338-353.
  • [18] Zadeh L.A., The concept of linguistic variable and its application to approximate reasoning. Inform. Sci., 8 (1975). 133-139.
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Sinem Tarsuslu Yılmaz

Mehmet Cıtıl

Publication Date June 1, 2019
IZ https://izlik.org/JA97JB45ZY
Published in Issue Year 2019 Volume: 32 Issue: 2

Cite

APA Tarsuslu Yılmaz, S., & Cıtıl, M. (2019). Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras. Gazi University Journal of Science, 32(2), 649-658. https://izlik.org/JA97JB45ZY
AMA 1.Tarsuslu Yılmaz S, Cıtıl M. Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras. Gazi University Journal of Science. 2019;32(2):649-658. https://izlik.org/JA97JB45ZY
Chicago Tarsuslu Yılmaz, Sinem, and Mehmet Cıtıl. 2019. “Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras”. Gazi University Journal of Science 32 (2): 649-58. https://izlik.org/JA97JB45ZY.
EndNote Tarsuslu Yılmaz S, Cıtıl M (June 1, 2019) Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras. Gazi University Journal of Science 32 2 649–658.
IEEE [1]S. Tarsuslu Yılmaz and M. Cıtıl, “Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras”, Gazi University Journal of Science, vol. 32, no. 2, pp. 649–658, June 2019, [Online]. Available: https://izlik.org/JA97JB45ZY
ISNAD Tarsuslu Yılmaz, Sinem - Cıtıl, Mehmet. “Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras”. Gazi University Journal of Science 32/2 (June 1, 2019): 649-658. https://izlik.org/JA97JB45ZY.
JAMA 1.Tarsuslu Yılmaz S, Cıtıl M. Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras. Gazi University Journal of Science. 2019;32:649–658.
MLA Tarsuslu Yılmaz, Sinem, and Mehmet Cıtıl. “Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras”. Gazi University Journal of Science, vol. 32, no. 2, June 2019, pp. 649-58, https://izlik.org/JA97JB45ZY.
Vancouver 1.Tarsuslu Yılmaz S, Cıtıl M. Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras. Gazi University Journal of Science [Internet]. 2019 June 1;32(2):649-58. Available from: https://izlik.org/JA97JB45ZY