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【期刊论文】Set Defuzzication and Choquet Integral
李寿梅, Shoumei Li Yukio Ogura Dan Ralescu
Published in 《International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems》 Vol. 123.(2001), 19-27,-0001,():
-1年11月30日
In this paper, we discuss the defuzzification problem. We first propose a set defuification method, (from a fuzzy set to a crisp set) by using the Aumann integral. From the obtained set to a point, we have two methods of defuzzification. One of these uses the mean value method and the other uses a fuzzy measure. In the first case, we compare our mean value method with the method of the center of gravity. In the second case, we compare fuzzy measure method with the Choquet integral method. We also give there a sufficient condition so that the results in the last two methods are equivalent.
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【期刊论文】Separability for Graph Convergence of Sequences of Fuzzy Valued Random Variables
李寿梅, Yukio Ogura Shoumei Li
Published in 《Fuzzy Sets and Systems》 Vol. 123. (2001), 19-27,-0001,():
-1年11月30日
We prove that the graph convergence in Hausdorff metric or Kuratowski-Mosco topology of a sequence of fuzzy sets follows from the conrgence of the sequences of the level sets for countable dense levels. As an application, we give a strong law of large numbers for fuzzy valued random variables, including the case when the level sets may not be bounded.
set valued random variable,, fuzzy valued random vari-able,, the Kuratowski-Mosco convergence,, the Hausdorff convergence,, convergence in graph.,
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【期刊论文】Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables
李寿梅, Shoumei Li Yukio Ogura Vladik Kreinovich
,-0001,():
-1年11月30日
Mathematical and Statistical Methods: Volume 43 This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as H
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【期刊论文】Laws of Large Numbers for weighted sums of fuzzy set-valued random variables
李寿梅
,-0001,():
-1年11月30日
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李寿梅, Shoumei Li a, *, Yukio Ogura b, , Hung. T. Nguyen c
Information Sciences 133(2001)7-21,-0001,():
-1年11月30日
The purpose of this paper is to discuss fuzzy valued Gaussian processes and mar-tingales with continuous parameter. We mainly obtain a representation theorem for fuzzy valued Gaussian processes after proving a new embedding theorem. Based on previous results about set valued and fuzzy valued martingales (cf. [S. Li, Y. Ogura, J. Fuzzy Math. 4 (1996) 905; S. Li, Y. Ogura, Fuzzy Sets and Systems 101 (1999) 453; S. Li, Y. Ogura, Ann. Probab. 26 (1998) 1384-1402; S. Li, Y. Ogura, in: Proc. IFSA '97, vol. 4, 1997, pp. 9-13; S. Li, Y. Ogura, in: C. Bertoluzza, M.A. Gil, D.A. Ralescu (Eds.), Statistical Modeling, Analysis and Management of Fuzzy Data, Physica (in press); Y. Ogura, S. Li, Fuzzy Sets and Systems (in press)]), we prove optional sampling theo- rems for set valued and fuzzy valued martingales with continuous parameter.
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