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On the existence of probability measures on fuzzy measurable spaces
Fuzzy Sets and Systems, 1991An \(F\)-quantum space [see the author and the reviewer, Fuzzy Sets Syst. 39, No. 1, 65-73 (1991)] is a couple \((X,M)\), where \(X\neq\emptyset\) and \(M\subset\langle 0,1\rangle^ X\) such that \(1_ X\in M\), \((1/2)_ X\not\in M\), \(f\in M\) implies \(1-f\in M\) and \(f_ n\in M\) \((n=1,2,\dots)\) implies \(\sup_ n f_ n\in M\). A probability on \(M\)
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Fuzzy subsets of the space of probability measures and expected value of fuzzy variable
Fuzzy Sets and Systems, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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FUZZY CONVERGENCE VERSUS WEAK CONVERGENCE IN SPACES OF PROBABILITY MEASURES
1984If X is a separable metrizable space, then on the set \({\mathcal M}(X)\) of all probability measures on X, the structure most frequently used is the weak topology, also called topology of weak convergence. In Math. Nachr. 115, 33-57 (1984; Zbl 0593.54006), the author introduced an alternative structure, a fuzzy topology, the topological modification ...
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On the Existence of Natural Fuzzy Topologies on Spaces of Probability Measures
Mathematische Nachrichten, 1984For a separable metric space X with metric topology \({\mathcal T}\), consider the set \({\mathcal M}(X)\) of all probability measures on the Borel \(\sigma\)- algebra on X. For a subbasis \({\mathcal S}\) of \({\mathcal T}\), the author constructs a natural fuzzy topology \(\Delta\) (X,\({\mathcal S})\) so that X is canonically homeomorphic to the set
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THE BAYES PRINCIPLE AND THE ENTROPY ON FUZZY PROBABILITY SPACES
International Journal of General Systems, 1991We present a fuzzy analogue of Bayes principle for general fuzzy probability spaces. Its validity leads to Piasecki's concept of a fuzzy probability space. For this type of fuzzy probability space, we define the notion of entropy and present fuzzy dynamical systems, their conjugation and isomorphism.
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Fuzzy Sets and Systems, 2000
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Conditional Events and Fuzzy Conditional Events Viewed from a Product Probability Space Perspective
1995This paper first provides a brief review of the product space approach to conditional event algebra and the one-point random set coverage function representation of fuzzy sets followed by a natural extension to a fuzzy set structure.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Multifunctional biomolecule nanostructures for cancer therapy
Nature Reviews Materials, 2021Jing Wang, Yiye Li, Guangjun Nie
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