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On the Atanassov Concept of Fuzziness and One of Its Modification

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Imprecision and Uncertainty in Information Representation and Processing

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 332))

Abstract

The family \(\mathcal F\) of intuitionistic fuzzy sets [1–3] is compared with the family \(\mathcal V\) of interval valued fuzzy sets. Since the spaces are isomorphic, from the measure theory on \(\mathcal F\) the measure theory on \(\mathcal V\) can be deduced. In the paper they are mentioned the state representation [7, 8, 44, 50], the inclusion—exclusion property [6, 22, 23] and the existence of invariant state [45].

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Acknowledgments

The support of the grant VEGA 1/0120/14 is kindly announced.

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Authors and Affiliations

  1. Faculty of Natural Sciences, Matej Bel University, Tajovsk ého 40, Bansk á Bystrica, Slovakia

    Beloslav Riečan

  2. Mathematical Institut, Slovak Academy of Sciences, Štef ánikova 49, Bratislava, Slovakia

    Beloslav Riečan

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  1. Beloslav Riečan
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Correspondence to Beloslav Riečan .

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  1. School of Computing and Communications, Lancaster University Bailrigg, Lancaster, United Kingdom

    Plamen Angelov

  2. Intelligent Systems Laboratory, Prof. Assen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

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Riečan, B. (2016). On the Atanassov Concept of Fuzziness and One of Its Modification. In: Angelov, P., Sotirov, S. (eds) Imprecision and Uncertainty in Information Representation and Processing. Studies in Fuzziness and Soft Computing, vol 332. Springer, Cham. https://doi.org/10.1007/978-3-319-26302-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-26302-1_3

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