| Convergence of Fuzzy Set Sequences |
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| 作者姓名： | 冯玉瑚 |
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| 作者单位： | Department of |
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| 摘 要： | There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper, common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or Dp*, 1≤p<∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comments on the convergence of LR-fuzzy number sequences are represented.
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Convergence of Fuzzy Set Sequences |
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| FENG Yu-hu.Convergence of Fuzzy Set Sequences[J].Journal of Donghua University,2002,19(4). |
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| Authors: | FENG Yu-hu |
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| Institution: | Department of Applied Mathematics, Dong Hua University, Shanghai, 200051 |
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| Abstract: | There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or D*p, 1 ≤ p ＜∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comme nts on the convergence of LRfuzzy number sequences are represented. |
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| Keywords: | Fuzzy set Hausdorff metric convergence relationship LR-fuzzy number |
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