ON INTERVAL VALUED INTUITIONISTIC FUZZY PAIRS

Year 2018, Volume: 1 Issue: 3 - To memory of Prof. RNDr. Beloslav Rieˇcan, DrSc., 261 - 268, 24.10.2018

Krassimir Atanassov Peter Vassilev Eulalia Szmidt Janusz Kacprzyk

Abstract

As was mentioned in [9], the first researches, related to Intuitionistic Fuzzy Sets (IFSs) started in 1983 and from the beginning, the concept of Intuitionistic Fuzzy Pair (IFP) had started to be

used. As we mentioned in [9], a lot of our colleagues working in the area of the intuitionistic fuzziness, used it without a special definition in many of their publications, using different names:

IFP, intuitionistic fuzzy couple, intuitionistic fuzzy value and others. In the mentioned paper, we proposed to the researchers in the area of the intuitionistic fuzziness to use only one name for the concept.

Keywords

Intuitionistic Fuzzy Sets, Intuitionistic Fuzzy Pair, IFS Operators, interval valued intuitionistic fuzzy pairs

References

• Angelova, N., M. Stoenchev. Intuitionistic fuzzy conjunctions and disjunctions from first type, Annual of “Informatics” Section, Union of Scientists in Bulgaria, Vol. 8, 2015/2016, 1-17.Atanassov, K. Intuitionistic Fuzzy Sets, Springer, Heldelberg, 1999.Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.Atanassov, K. Intuitionistic fuzzy logics as tools for evaluation of Data Mining processes,Knowledge-Based Systems, Vol. 80, 2015, 122-130.Atanassov, K. Intuitionistic fuzzy modal operators of second type over interval-valued intuitionistic fuzzy sets. Part 1, Notes on Intuitionistic Fuzzy Sets, Vol. 24, 2018, No. 2, 8-17. 7Atanassov, K. Intuitionistic fuzzy modal operators of second type over interval-valued intuitionistic fuzzy sets. Part 2, Notes on Intuitionistic Fuzzy Sets, Vol. 24, 2018, No. 3 (in press).Atanassov, K. On the Most Extended Modal Operator of First Type over Interval-Valued Intuitionistic Fuzzy Sets. Mathematics 2018, 6, 123; doi:10.3390/math6070123Atanassov, K.On the two most extended modal types of operators defined over interval valued intuitionistic fuzzy sets. Annals of Fuzzy Mathematics and Informatics (in press).Atanassov, K., E. Szmidt, J. Kacprzyk. On intuitionistic fuzzy pairs, Notes on Intuitionistic Fuzzy Sets, Vol. 19, 2013, No. 3, 1-13.Atanassov, K., Szmidt, E., Kacprzyk, J., Vassilev, P. On intuitionistic fuzzy pairs of n-th type. Issues in IFSs and GNs, 13, 2017, ISBN:978-83-61551-21-8, 136-142.Çuvalcıoğlu, G., Some properties of E; operator. Advanced Studies in Contemporary Mathematics, Vol. 14, 2007, No. 2, 305-310.Feys R. Modal Logics, Gauthier-Villars, Paris, 1965.Szmidt, E., Distances and Similarities in Intuitionistic Fuzzy Sets, Springer, Berlin, 2014.Vassilev, P., Ribagin, S., Kacprzyk, J. (2018) A remark on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 24 (2), 1-7, doi: 10.7546/nifs.2018.24.2.1-78