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Measures of uncertainty for a fuzzy probabilistic approximation space
Journal of Intelligent & Fuzzy Systems, 2022An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space.
Lijun Chen +4 more
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Fuzzy regular measures on topological spaces
Fuzzy Sets and Systems, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianrong Wu, Congxin Wu
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Fuzzy Measure Spaces Generated by Fuzzy Sets
2010In this paper we study fuzzy measures which are defined on algebras of fuzzy subsets of a given fuzzy set. Subsequently, we use these fuzzy measures to define a fuzzy integral. We show basic properties of these fuzzy measures and integrals. We are motivated by our research on fuzzy quantifiers, where this fuzzy integral is used.
Antonín Dvorák, Michal Holcapek
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Measures of noncompactness for fuzzy sets in fuzzy topological spaces
Fuzzy Sets and Systems, 2000Recently \textit{S. G. Gal} introduced and studied some measures of non-compactness for fuzzy subsets of metric and fuzzy metric spaces [J. Fuzzy Math. 2, No. 3, 623-634 (1994; Zbl 0818.54006); 3, No. 4, 941-947 (1995; Zbl 0870.54006); 5, No. 2, 309-320 (1997; Zbl 0890.54006)]. On the other hand, \textit{I. Kupka} and \textit{V.
Adrian I. Ban, Sorin G. Gal
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Measures of compactness in L-fuzzy pretopological spaces
Journal of Intelligent & Fuzzy Systems, 2014In this paper, we introduce the concepts of the degrees of compactness, countable compactness and Lindelöf property in L-fuzzy pretopological spaces by means of implication operator. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required.
Fu-Gui Shi, Chengyu Liang
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A further investigation for fuzzy measures on metric spaces
Fuzzy Sets and Systems, 1999A set function \(m: B\to [0,\infty]\) defined on the family of all Borel subsets of a metric space is an LSC-fuzzy measure if \(m(\emptyset)=0\), \(m\) is monotone and continuous from below. It is said to be exhaustive if \(\lim m(E_n)= 0\) for any disjoint sequence \((E_n)\).
Qingshan Jiang +2 more
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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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Fuzzy probabilistic approximation spaces and their information measures
IEEE Transactions on Fuzzy Systems, 2006Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model.
Qinghua Hu +3 more
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On Egoroff's theorems on fuzzy measure spaces
Fuzzy Sets and Systems, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Notes on Riesz's theorem on fuzzy measure space
Fuzzy Sets and Systems, 1997A fuzzy measure is considered as a non-negative function, zero in the empty set, monotone and continuous. A necessary and sufficient condition is given for every sequence of non-negative finite measurable functions converging in measure to contain a subsequence converging a.e.
Minghu Ha 0001, Lixin Cheng, Xizhao Wang
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