Comments on crucial and unsolved problems on Atanassov’s intuitionistic fuzzy sets
- 60 Downloads
In the paper Crucial and unsolved problems on Atanassov’s intuitionistic fuzzy sets, D.-F. Li pointed out that some kind of definitions of operations over Atanassov’s intuitionistic fuzzy sets are incorrect. We can see that, near 30 years after the first Atanassov’s papers, there exist some misunderstandings related not only on the name, but also on the basic operations on IFSs. Those misunderstandings concern, this time, on the operations of the sum and product. Li also casts doubt the equivalence of the intuitionistic fuzzy sets and the interval-valued fuzzy sets. In this paper, the Li’s reasoning is presented and commented.
KeywordsIntuitionistic fuzzy sets (IFSs) Operations on IFSs Extension principle for IFSs Interval-valued fuzzy sets
Compliance with ethical standards
Conflict of interest
Author P. Dworniczak declares that he has no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Cornelis C, Deschrijver G (2001) The compositional rule of inference in an intuitionistic fuzzy logic setting (cited also as: The compositional rule of inference in an intuitionistic fuzzy logic framework). In: Striegnitz K (ed) Proceedings of ESSLLI 2001, student session. pp 83–94Google Scholar
- Cornelis C, Deschrijver G, Kerre EE (2002) Classification of intuitionistic fuzzy implicators an algebraic approach. In: Proceedings of the FT&T’02, 8th international conference on fuzzy theory and technology, March 9–12, 2002, pp 105–108. DurhamGoogle Scholar
- Dworniczak P (2018) Some remarks about Crucial and unsolved problems on Atanassov’s intuitionistic fuzzy sets. In: Kacprzyk J, Szmidt E, Zadrożny S, Atanassov K, Krawczak M (eds) Advances in fuzzy logic and technology 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham, pp 684–688Google Scholar
- Stoeva M (1999) Intuitionistic fuzzy extension principle. Notes on Intuit Fuzzy Sets, 5(3):29–30Google Scholar