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Soft Computing

, Volume 22, Issue 15, pp 4935–4939 | Cite as

Comments on crucial and unsolved problems on Atanassov’s intuitionistic fuzzy sets

  • Piotr Dworniczak
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Abstract

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.

Keywords

Intuitionistic fuzzy sets (IFSs) Operations on IFSs Extension principle for IFSs Interval-valued fuzzy sets 

Notes

Compliance with ethical standards

Conflict of interest

Author P. Dworniczak declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Great Poland University of Social and EconomicsŚroda WielkopolskaPoland

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