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Issue:The Pickands–Balkema–de Haan theorem for intuitionistic fuzzy events

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Title of paper: The Pickands–Balkema–de Haan theorem for intuitionistic fuzzy events
Katarína Čunderlíková
Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia
Renáta Bartková
Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, 974 01 Banská Bystrica, Slovakia
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 2, pages 63-75
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Abstract: In the paper the space of observables with respect to a family of the intuitionistic fuzzy events is considered. We proved the modification of the Fisher–Tippett–Gnedenko theorem for sequence of independent intuitionistic fuzzy observables in paper [3]. Now we prove the

modification of the Pickands–Balkema–de Haan theorem. Both are theorems of part of statistic, which is called the extreme value theory.

Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy state, Sequence of intuitionistic fuzzy observables, Joint intuitionistic fuzzy observable, Excess intuitionistic fuzzy distribution, Maximum domain of attraction for intuitionistic fuzzy case, Generaized Pareto distribution, Pickands–Balkema–de Haan theorem, Extreme value theory.
AMS Classification: 03F55, 94D05, 03E72, 60B10, 60B12, 62E17, 62G32
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