Results 221 to 230 of about 4,356,350 (249)

Probability measures over fuzzy spaces

International Journal of General Systems, 2007
A 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
openaire   +1 more source

On Egoroff's theorems on fuzzy measure spaces

Fuzzy Sets and Systems, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

The fuzzy integral on product spaces for NSA measures

Fuzzy Sets and Systems, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E. Suárez Díaz, F. Suárez García
openaire   +3 more sources

Fuzzy probabilistic approximation spaces and their information measures

IEEE Transactions on Fuzzy Systems, 2006
Rough 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, Daren Yu, Zongxia Xie, Jinfu Liu   +3 more
openaire   +1 more source

Notes on Riesz's theorem on fuzzy measure space

Fuzzy Sets and Systems, 1997
A 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
openaire   +2 more sources

A further investigation for fuzzy measures on metric spaces

Fuzzy Sets and Systems, 1999
A 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, Shengrui Wang, Djemel Ziou   +2 more
openaire   +2 more sources

On the extension of the fuzzy number measures in Banach spaces: Part I. Representation of the fuzzy number measures

Fuzzy Sets and Systems, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoping Xue 0001, Minghu Ha 0001, Congxin Wu   +2 more
openaire   +2 more sources

Fuzzy metrization of the spaces of idempotent measures

European Journal of Mathematics, 2019
There exists the notion of fuzzy metric space of [\textit{I. Kramosil} and \textit{J. Michalek}, Kybernetika 11, 336--344 (1975; Zbl 0319.54002)] motivated by the concept of statistical metric space of [\textit{B. Schweizer} and \textit{A. Sklar}, Pac. J. Math. 10, 313--334 (1960; Zbl 0091.29801)].
Brydun, Viktoriya, Savchenko, Aleksandr, Zarichnyi, Mykhailo   +2 more
openaire   +2 more sources

Measures of fuzzy semicompactness in $L$-fuzzy topological spaces

2013
In this paper, the notion of fuzzy semicompactness degrees is in- troduced in L-fuzzy topological spaces by means of the implication operation of L. Characterizations of fuzzy semicompactness degrees in L-fuzzy topologi- cal spaces are obtained, and some properties of fuzzy semicompactness degrees are researched.
Yang, Wen-Hua, Li, Sheng-Gang, Zhao, Hu
openaire   +1 more source

Regularity of fuzzy measures on complete and separable metric spaces

Journal of Intelligent & Fuzzy Systems, 2016
The regularity of continuous fuzzy measures on complete separable metric spaces are discussed. It is shown that a finite continuous fuzzy measure is tight on complete and separable metric spaces, and if the fuzzy measure is weakly null-additive, then it is regular.
Shan Cao 0005, Yuhuan Wang, Jun Li
openaire   +2 more sources