The Experts below are selected from a list of 69 Experts worldwide ranked by ideXlab platform

Meng-ke Bian - One of the best experts on this subject based on the ideXlab platform.

  • Characterizations of the Borel \(\sigma\)-Fields of the fuzzy number space
    ANZIAM Journal, 2017
    Co-Authors: Tai-he Fan, Meng-ke Bian
    Abstract:

    In this paper, we characterize Borel \(\sigma\)-Fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel \(\sigma\)-Fields with respect to all known separable metrics are identical. This Borel Field is the Borel \(\sigma\)-Field making all level cut functions of fuzzy mappings from any measurable spaces to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel \(\sigma\)-Field with respect to the supremum metric \(d_{\infty}\) is also demonstrated. We prove that the Borel Field is induced by a separable and complete metric. A global characterization of measurability of fuzzy valued functions is given via the main result. Applications to fuzzy valued integral are given, and an approximation method is presented for integrals of fuzzy valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied Fields. doi:10.1017/S1446181117000189

  • CHARACTERIZATIONS OF THE Borel -FieldS OF THE FUZZY NUMBER SPACE
    The ANZIAM Journal, 2017
    Co-Authors: Tai-he Fan, Meng-ke Bian
    Abstract:

    In this paper, we characterize Borel $\unicode[STIX]{x1D70E}$-Fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel $\unicode[STIX]{x1D70E}$-Fields with respect to all known separable metrics are identical. This Borel Field is the Borel $\unicode[STIX]{x1D70E}$-Field making all level cut functions of fuzzy mappings from any measurable space to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel $\unicode[STIX]{x1D70E}$-Field with respect to the supremum metric $d_{\infty }$ is also demonstrated. We prove that the Borel Field is induced by a separable and complete metric. A global characterization of measurability of fuzzy-valued functions is given via the main result. Applications to fuzzy-valued integrals are given, and an approximation method is presented for integrals of fuzzy-valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied Fields.

Tai-he Fan - One of the best experts on this subject based on the ideXlab platform.

  • Characterizations of the Borel \(\sigma\)-Fields of the fuzzy number space
    ANZIAM Journal, 2017
    Co-Authors: Tai-he Fan, Meng-ke Bian
    Abstract:

    In this paper, we characterize Borel \(\sigma\)-Fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel \(\sigma\)-Fields with respect to all known separable metrics are identical. This Borel Field is the Borel \(\sigma\)-Field making all level cut functions of fuzzy mappings from any measurable spaces to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel \(\sigma\)-Field with respect to the supremum metric \(d_{\infty}\) is also demonstrated. We prove that the Borel Field is induced by a separable and complete metric. A global characterization of measurability of fuzzy valued functions is given via the main result. Applications to fuzzy valued integral are given, and an approximation method is presented for integrals of fuzzy valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied Fields. doi:10.1017/S1446181117000189

  • CHARACTERIZATIONS OF THE Borel -FieldS OF THE FUZZY NUMBER SPACE
    The ANZIAM Journal, 2017
    Co-Authors: Tai-he Fan, Meng-ke Bian
    Abstract:

    In this paper, we characterize Borel $\unicode[STIX]{x1D70E}$-Fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel $\unicode[STIX]{x1D70E}$-Fields with respect to all known separable metrics are identical. This Borel Field is the Borel $\unicode[STIX]{x1D70E}$-Field making all level cut functions of fuzzy mappings from any measurable space to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel $\unicode[STIX]{x1D70E}$-Field with respect to the supremum metric $d_{\infty }$ is also demonstrated. We prove that the Borel Field is induced by a separable and complete metric. A global characterization of measurability of fuzzy-valued functions is given via the main result. Applications to fuzzy-valued integrals are given, and an approximation method is presented for integrals of fuzzy-valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied Fields.

George J. Klir - One of the best experts on this subject based on the ideXlab platform.

Zhenyuan Wang - One of the best experts on this subject based on the ideXlab platform.

Jaime A. Londoño - One of the best experts on this subject based on the ideXlab platform.

  • An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit
    Journal of Probability and Statistics, 2017
    Co-Authors: Jaime A. Londoño
    Abstract:

    For a Polish Sample Space with a Borel -Field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets, where each limiting distribution is the unique ergodic probability measure defined on each set. The results obtained suggest some natural objects for the model of a probabilistic time-invariant phenomenon are uniquely ergodic probability spaces. As a consequence of the results gained in this paper, we propose a notion of randomness that is weaker than recent approaches to Schnorr randomness.