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On fuzziness in a probability space
Journal of Discrete Mathematical Sciences and Cryptography, 1998Abstract Our main purpose here is to introduce the concepts of fuzzy theory and its impact on Probability structure. We develop here Fuzzy probability algebra and derive theorems analogous to its classical approach. We extend here the Czogala and Wrocinski [1] approach to seperativity between fuzzy subsets and derive Bayes formula based on complete ...
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Affinity and class probability-based fuzzy support vector machine for imbalanced data sets
Neural Networks, 2019The learning problem from imbalanced data sets poses a major challenge in data mining community. Although conventional support vector machine can generally show relatively robust performance in dealing with the classification problems of imbalanced data ...
Xinmin Tao +6 more
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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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Fuzzy and probability vectors as elements of a vector space
Information Sciences, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shvaytser, Haim, Peleg, Shmuel
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Melting Probability Measure With OWA Operator to Generate Fuzzy Measure: The Crescent Method
IEEE transactions on fuzzy systems, 2019Given probability information, i.e., a probability measure m with a random variable x on the outcome space N, the expected value of that random variable is commonly used as some valuable evaluation result for further decision making. However, there is no
Lesheng Jin, R. Mesiar, R. Yager
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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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Solving fuzzy linear systems in Gaussian PDMF space
Fuzzy Sets Syst.We solve the fuzzy linear systems in a fuzzy number space $\mathcal{X}$, namely the Gaussian probability density membership function (Gaussian-PDMF) space.
Chuang Zheng
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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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