Probabilistic Fuzzy Sets and a Related Operator Algebra |
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| Authors: | M. Arik F. Torunbalc Aydin |
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| Affiliation: | (1) Department of Physics, Boğaziçi University, Faculty of Arts and Sciences, 34342 Bebek, Istanbul, Turkey;(2) Engineering Mathematics Department, Yıldız Technical University, Davutpaşa, Istanbul, Turkey |
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| Abstract: | The rules of union and intersection of probabilistic fuzzy sets guided us to construct a related operator algebra. In a Hilbert space, where each fuzzy set is represented by an orthonormal vector, the union and the intersection operators generate a well-defined algebra with a unique representation. PACS NUMBER: 02.10.-v |
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| Keywords: | quantum physics Hilbert space fuzzy sets random sets q-oscillator operator algebra |
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