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A Perspective on Differences Between Atanassov’s Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets

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Fuzzy Sets, Rough Sets, Multisets and Clustering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 671))

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Abstract

In the paper we show our perspective on some differences between Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short) and Interval-valued fuzzy sets (IVFSs, for short). First, we present some standard operators and extensions for the A-IFSs which have no counterparts for IVFSs. Next, we show on an example a practical application based on one of such operators. We also revisit, and further analyze, the concepts of two possible representations of A-IFSs: the two term one, in which the degrees of membership and non-membership are only involved, and the three term one, in which in addition to the above degrees of membership and non-membership the so called hesitation margin is explicitly accounted for. Though both representations are mathematically correct and may be considered equivalent, the second one involves explicitly an additional, conceptually different information than the degree of membership and non-membership only even if it directly results from these two degrees. We then show on some examples of decision making type problems its intuitive appeal and usefulness for reflecting more sophisticated intentions and preferences of the user which cannot be fully reflected via their counterpart IVFSs based models. Finally, we recall different measures that are important from the point of view of applications. We consider the measures for both types representations of the A-IFSs pointing out some further differences in comparison to the case of the IVFSs.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Eulalia Szmidt

  2. Warsaw School of Information Technology, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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  1. Eulalia Szmidt
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  2. Janusz Kacprzyk
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Correspondence to Eulalia Szmidt .

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Editors and Affiliations

  1. University of Skövde, School of Informatics University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. University of Skövde, School of Informatics University of Skövde, Skövde, Sweden

    Anders Dahlbom

  3. Toho Gakuen , Tokyo, Japan

    Yasuo Narukawa

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Szmidt, E., Kacprzyk, J. (2017). A Perspective on Differences Between Atanassov’s Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets. In: Torra, V., Dahlbom, A., Narukawa, Y. (eds) Fuzzy Sets, Rough Sets, Multisets and Clustering. Studies in Computational Intelligence, vol 671. Springer, Cham. https://doi.org/10.1007/978-3-319-47557-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-47557-8_13

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