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On modal operators over the generalized intuitionistic fuzzy set

Year 2018, Volume: 31 Issue: 1, 222 - 234, 01.03.2018

Abstract

In recent years, different operators (modal, topological, level, negation and other types) have been

defined over intuitionistic fuzzy sets. In this note, modal type of operators over an extended generalized

intuitionistic fuzzy set GIFSB are proposed. Some of the basic properties of the new
operators are derived.

References

  • [1] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96. [2] Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33, 37-45. [3] Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets. Springer Verlag, Heidelberg. [4] Atanassov, K. T. (2001). On four intuitionistic fuzzy topological operators. Mathware Soft Computing, 8, 65-70. [5] Atanassov, K. T. (2004). On the modal operators deferent over the intuitionistic fuzzy set. Notes on Intuitionistic Fuzzy Sets, 10, 7-12. [6] Atanassov, K. T. (2012). On the operators partially extending the extended intuitionistic fuzzy operators from modal type. Notes on Intuitionistic Fuzzy Sets, 18, 16-22. [7] Atanassov, K. T., Dimitrov, D. (2008). On the negations over intuitionistic fuzzy sets. Annual of \Informatics" Section Union of Scientists in Bulgaria, 1, 49-58. [8] Baloui Jamkhaneh, E., Nadarajah, S. (2015). A new generalized intuitionistic fuzzy sets. Hacettepe Journal of Mathematics and Statistics, 44, 1537-1551. [9] Cornelis, C., Kerre, E., Atanassov, K. (2004). Application of extended modal operators as a tool for constructing inclusion indicators over intuitionistic fuzzy sets. In: Soft Computing- Foundations and Theoretical Aspects, pp. 133-142. [10] Hinde, C. J., Atanassov, K. T. (2008). On intuitionistic fuzzy negations and intuitionistic fuzzy modal operators with contradictory evidence. In Proceedings of the 5th WSEAS / IASME International Conference on Engineering Education (EE'08), Heraklion, Greece, July 22-24. [11] Parvathi, R., Geetha, S. P. (2009). A note on properties of temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 15, 42-48. [12] Sharma, P. K. (2014). Modal operator F ; (A) in intuitionistic fuzzy groups. Annals of Pure and Applied Mathematics, 7, 19-28. [13] Srinivasan, R., Palaniappan, N. (2012). Some operators on intuitionistic fuzzy sets of root type. Annals of Fuzzy Mathematics and Informatics, 4, 377-383. [14] Yilmaz, S., Cuvalcioglu, G. (2014). On level operators for temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 20, 6-15.
Year 2018, Volume: 31 Issue: 1, 222 - 234, 01.03.2018

Abstract

References

  • [1] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96. [2] Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33, 37-45. [3] Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets. Springer Verlag, Heidelberg. [4] Atanassov, K. T. (2001). On four intuitionistic fuzzy topological operators. Mathware Soft Computing, 8, 65-70. [5] Atanassov, K. T. (2004). On the modal operators deferent over the intuitionistic fuzzy set. Notes on Intuitionistic Fuzzy Sets, 10, 7-12. [6] Atanassov, K. T. (2012). On the operators partially extending the extended intuitionistic fuzzy operators from modal type. Notes on Intuitionistic Fuzzy Sets, 18, 16-22. [7] Atanassov, K. T., Dimitrov, D. (2008). On the negations over intuitionistic fuzzy sets. Annual of \Informatics" Section Union of Scientists in Bulgaria, 1, 49-58. [8] Baloui Jamkhaneh, E., Nadarajah, S. (2015). A new generalized intuitionistic fuzzy sets. Hacettepe Journal of Mathematics and Statistics, 44, 1537-1551. [9] Cornelis, C., Kerre, E., Atanassov, K. (2004). Application of extended modal operators as a tool for constructing inclusion indicators over intuitionistic fuzzy sets. In: Soft Computing- Foundations and Theoretical Aspects, pp. 133-142. [10] Hinde, C. J., Atanassov, K. T. (2008). On intuitionistic fuzzy negations and intuitionistic fuzzy modal operators with contradictory evidence. In Proceedings of the 5th WSEAS / IASME International Conference on Engineering Education (EE'08), Heraklion, Greece, July 22-24. [11] Parvathi, R., Geetha, S. P. (2009). A note on properties of temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 15, 42-48. [12] Sharma, P. K. (2014). Modal operator F ; (A) in intuitionistic fuzzy groups. Annals of Pure and Applied Mathematics, 7, 19-28. [13] Srinivasan, R., Palaniappan, N. (2012). Some operators on intuitionistic fuzzy sets of root type. Annals of Fuzzy Mathematics and Informatics, 4, 377-383. [14] Yilmaz, S., Cuvalcioglu, G. (2014). On level operators for temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 20, 6-15.
There are 1 citations in total.

Details

Journal Section Mathematics
Authors

Ezzatallah Baloui Jamkhaneh

Saralees Nadarajah

Publication Date March 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 1

Cite

APA Baloui Jamkhaneh, E., & Nadarajah, S. (2018). On modal operators over the generalized intuitionistic fuzzy set. Gazi University Journal of Science, 31(1), 222-234.
AMA Baloui Jamkhaneh E, Nadarajah S. On modal operators over the generalized intuitionistic fuzzy set. Gazi University Journal of Science. March 2018;31(1):222-234.
Chicago Baloui Jamkhaneh, Ezzatallah, and Saralees Nadarajah. “On Modal Operators over the Generalized Intuitionistic Fuzzy Set”. Gazi University Journal of Science 31, no. 1 (March 2018): 222-34.
EndNote Baloui Jamkhaneh E, Nadarajah S (March 1, 2018) On modal operators over the generalized intuitionistic fuzzy set. Gazi University Journal of Science 31 1 222–234.
IEEE E. Baloui Jamkhaneh and S. Nadarajah, “On modal operators over the generalized intuitionistic fuzzy set”, Gazi University Journal of Science, vol. 31, no. 1, pp. 222–234, 2018.
ISNAD Baloui Jamkhaneh, Ezzatallah - Nadarajah, Saralees. “On Modal Operators over the Generalized Intuitionistic Fuzzy Set”. Gazi University Journal of Science 31/1 (March 2018), 222-234.
JAMA Baloui Jamkhaneh E, Nadarajah S. On modal operators over the generalized intuitionistic fuzzy set. Gazi University Journal of Science. 2018;31:222–234.
MLA Baloui Jamkhaneh, Ezzatallah and Saralees Nadarajah. “On Modal Operators over the Generalized Intuitionistic Fuzzy Set”. Gazi University Journal of Science, vol. 31, no. 1, 2018, pp. 222-34.
Vancouver Baloui Jamkhaneh E, Nadarajah S. On modal operators over the generalized intuitionistic fuzzy set. Gazi University Journal of Science. 2018;31(1):222-34.