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Issue:Connection between interval-valued observables and intuitionistic fuzzy observables

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Title of paper: Connection between interval-valued observables and intuitionistic fuzzy observables
Katarína Čunderlíková
Mathematical Institute, Slovak Academy of Sciences, 49 Stefánikova Str., 814 73 Bratislava, Slovakia
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 1, pages 32–42
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Abstract: In paper [4] the authors studied probability on two lattices and they showed that these two lattices are isomorphic. First lattice was the geometrical interpretation of intuitionistic fuzzy sets introduced by K. T. Atanassov and the second lattice was the geometrical interpretation of interval valued sets introduced by L. A. Zadeh. Later in papers [3, 6] authors studied intuitionistic fuzzy events and interval-valued events. They showed that these two systems are isomorphic and they illustrated the connection between intuitionistic fuzzy state and interval valued state. In this paper, we define the notion of interval valued observable and we display the connection to the intuitionistic fuzzy observable. We define the notion of interval valued mean value and dispersion and we show the relation between interval-valued distribution function and intuitionistic fuzzy distribution function, too.
Keywords: Intuitionistic fuzzy set, Interval-valued set, Intuitionistic fuzzy event, Interval-valued event, Intuitionistic fuzzy state, Interval-valued state, Intuitionistic fuzzy observable, Interval-valued observable, Isomorphism, Interval-valuedmeanvalue, Interval-valueddispersion, Interval-valued distribution function, Intuitionistic fuzzy distribution function.
AMS Classification: 03E72, 03B52, 60A86.
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