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Probability theory in fuzzy sample spaces
Metrika, 2004This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of Open image in new window The investigations are focussed on the discussion how to equip those sample spaces with suitable σ-algebras and metrics.
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IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028), 2003
Proposes an idea for the problem of how to rationally qualify the probability measure for a vague event in a vague sample space after a subject considers the event and the sample space, and clarifies the vagueness by use of his subjective judgment and fuzzy sets theory.
Y. Kato +3 more
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Proposes an idea for the problem of how to rationally qualify the probability measure for a vague event in a vague sample space after a subject considers the event and the sample space, and clarifies the vagueness by use of his subjective judgment and fuzzy sets theory.
Y. Kato +3 more
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Fuzzy probability spaces defined by means of the fuzzy relation ‘less than’
Fuzzy Sets and Systems, 1986In this paper a fuzzy relation ''less than'' and fuzzy probability spaces on the real line are defined. Fuzzy \(\sigma\)-algebras of events are introduced in an analogous way to the classical theory of probability by means of the above relation. Furthermore, specific properties of the fuzzy probability measures presented here are given.
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New Fuzzy Probability Spaces and Fuzzy Random Variables Based on Gradual Numbers
2014In this paper, we deal with special generalization of probability measures and random variables by considering their values in the set of gradual numbers. Firstly, the concept of gradual probability measures is introduced and some of its properties are discussed.
Cai-Li Zhou, Peng Wang
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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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Probability measures on fuzzy events in phase space
Journal of Mathematical Physics, 1976The notion of fuzzy sample point is introduced, and generalized probability measures on fuzzy events are defined. This leads to the concept of spectral measure on fuzzy events. It is shown that such measures can be associated with quantum-mechanical states when the fuzzy elementary events are represented by Gaussian distributions on phase space.
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Journal of Intelligent & Fuzzy Systems, 2018
Three way decision model, as a new and meaningful decision making method, has attracted much attention and various results and applications have been reported. This paper investigates decision-theoretic rough set (DTRS) approach in the framework of multi-covering approximation spaces.
Liu, Caihui +3 more
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Three way decision model, as a new and meaningful decision making method, has attracted much attention and various results and applications have been reported. This paper investigates decision-theoretic rough set (DTRS) approach in the framework of multi-covering approximation spaces.
Liu, Caihui +3 more
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The conjugation of fuzzy probability spaces to the unit interval
Fuzzy Sets and Systems, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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The Radon-Nikodým theorem for fuzzy probability spaces
Fuzzy Sets and Systems, 1992The Radon-Nikodým theorem is proved for fuzzy observables. Some possibilities of applications are given. In my opinion, the signed measure is not a real generalization of fuzzy \(P\)-measure because of: at the first --- the case \(m(\mathbf{1}_ x)=0\) is not interested; at the second --- for each signed measure \(m\) such that \(m(\mathbf{1}_ x)
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