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Fuzzy probability over fuzzy -field with fuzzy topological spaces
Fuzzy Sets and Systems, 2000In the classical paper [J. Math. Anal. Appl. 23, 421-427 (1968; Zbl 0174.49002)] \textit{L. A. Zadeh} defined a probability of a fuzzy event \(\mu:\Omega\to [0,1]\) as \(m(\mu)=\int \mu dP\), where \((\Omega,\mathcal{F},P)\) is a classical probability space. Since then many authors have generalized this definition into different directions.
Jershan Chiang, Jing-Shing Yao
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Correlation of intuitionistic fuzzy sets in probability spaces
Fuzzy Sets and Systems, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dug Hun Hong, Seok Yoon Hwang
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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.
Haim Shvaytser, Shmuel Peleg
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Fuzzy probability system: fuzzy-probability space (1)
Fuzzy Sets and Systems, 2001Abstract The present paper discusses “The major objective of the theory of probability”, and hence provides a fuzzy probability system, which links both Von Mises's probability system and Kolmogorov's probability system to be a new one. Such a probability system has a more original theoretical starting point, and appears to deal with such uncertainty
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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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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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Probability measures over fuzzy spaces
International Journal of General Systems, 2007A probability measure is defined on subsets of an underlying space. In classical probability theory, both the underlying space and the subsets whose probabilities we measure are crisp subsets. Zadeh provided an extension of this to the case in which the subsets whose probabilities we are measuring can be fuzzy. Here, we provide a further generalization
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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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