Saralees NADARAJAH, Ezzatallah BALOUI JAMKHANEH

On Modal Operators over the Generalized Intuitionistic Fuzzy Set

In recent years, different operators (modal, topological, level, negation and other types) havebeen defined over intuitionistic fuzzy sets. In this note, modal types of operators over anextended generalized intuitionistic fuzzy set GIFSB are proposed. Some of the basic propertiesof the new operators are derived.

PDF

___

Atanassov, K.T., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20(1): 87-96, (1986).
Atanassov, K.T., “Intuitionistic fuzzy sets”, Springer Physica-Verlag, Heidelberg, (1999).
Atanassov, K.T., “More on intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 33: 37-45, (1989).
Atanassov, K.T., “On four intuitionistic fuzzy topological operators”, Math Ware Soft Comput., 8: 65-70, (2001).
Atanassov, K.T., “On the modal operators deferent over the intuitionistic fuzzy set”, Notes on Intuitionistic Fuzzy Sets, 10(1): 7-12, (2004).
Cornelis, C., Atanassov, K.T., Kerre, E., “Application of extended modal operators as a tool for constructing inclusion indicators over intuitionistic fuzzy sets”, Soft Computing-Foundations and Theoretical Aspects., 133-142, (2004).
Atanassov, K.T., Dimitrov, D., “On the negations over intuitionistic fuzzy sets”, Annual of "Informatics" Section Union of Scientists in Bulgaria, 1: 49-58, (2008).
Hinde, C.J., Atanassov, K.T., “On intuitionistic fuzzy negations and intuitionistic fuzzy modal operators with contradictory evidence”, 5th WSEAS / IASME International Conference on Engineering Education (EE'08), Heraklion, Greece, July 22-24, (2008).
Parvathi, R., Geetha, S.P., “A note on properties of temporal intuitionistic fuzzy sets”, Notes on Intuitionistic Fuzzy Sets, 15(1): 42–48, (2009).
Atanassov, K.T., “On the operators partially extending the extended intuitionistic fuzzy operators from modal type”, Notes on Intuitionistic Fuzzy Sets, 18(3): 16–22, (2012).
Srinivasan, R., Palaniappan, N., “Some operators on intuitionistic fuzzy sets of root type”, Annals of Fuzzy Mathematics and Informatics, 4(2): 377-383, (2012).
Sharma, P.K., “Modal operator Fα,β (A)in intuitionistic fuzzy groups”, Annals of Pure and Applied Mathematics, 7(1): 19-28, (2014).
Yilmaz, S., Cuvalcioglu, G., “On level operators for temporal intuitionistic fuzzy sets”, 18th Int. Conf. on IFSs, Sofia, 10–11 May 2014, Notes on Intuitionistic Fuzzy Sets, 20(2): 6–15, (2014).
Baloui Jamkhaneh, E., Nadarajah, S., “A new generalized intuitionistic fuzzy sets”, Hacettepe Journal of Mathematics and Statistics, 44 (6): 1537–1551, (2015).
Baloui Jamkhaneh, E., “The operators over the generalized intuitionistic fuzzy sets”, International Journal of Nonlinear Analysis and Applications, 8(1): 11-21, (2017).
Baloui Jamkhaneh, E., Nadi Ghara A., “Four new operators over generalized intuitionistic fuzzy sets”, Journal of New Theory, 18: 12-21, (2017).
Baloui Jamkhaneh, E., Garg, H., “Some new operations over the generalized intuitionistic fuzzy sets and their application to decision making process”, Granular Computing, DOI 10.1007/s41066-017- 0059-0, (2017).