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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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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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The Spaces of Fuzzy Probability and Possibility (I)
1983Zadeh1, 1978, pointed out that Fuzzy Sets’ theory can be a basis for a theory of possibility, which is similar to the role of measure theory for probability theory. He put emphasis on the fact that a variable usually relates with both probability distribution and possibility distribution.
Zhende Huang, Tong Zhengxiang
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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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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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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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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.
Caili Zhou, Peng Wang
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International Journal of Fuzzy Computation and Modelling, 2016
Random variable basically addresses a probability space and fuzzy random variable (FRV) will address the fuzzy probability space. Concepts of FRV valued functions such as exponential function, logarithmic function and power function have been already researched.
Rituparna Chutia, D. Datta
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Random variable basically addresses a probability space and fuzzy random variable (FRV) will address the fuzzy probability space. Concepts of FRV valued functions such as exponential function, logarithmic function and power function have been already researched.
Rituparna Chutia, D. Datta
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Probability Theory for Fuzzy Quantum Spaces with Statistical Applications
2017The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications ...
Renáta Bartková +2 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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