| 关于《完备Brouwer格上伪t-模与蕴涵算子》的注记 |
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| 引用本文： | 韩成哲,李洪兴.关于《完备Brouwer格上伪t-模与蕴涵算子》的注记[J].模糊系统与数学,2006,20(1):103-106. |
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| 作者姓名： | 韩成哲 李洪兴 |
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| 作者单位： | 1. 金日成综合大学,数学力学系,朝鲜,平壤;北京师范大学,数学科学学院,北京,100875
2. 北京师范大学,数学科学学院,北京,100875 |
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| 基金项目： | National Natural Science Foundation of China(60474023)，Research Fund for Doctoral Program of
Higher Education(20020027013)，Science and Technology Key Project Fund of Ministry of Education(03184)，Major State Basic
Research Development Program of China(2002CB312200) |
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| 摘 要： | 举例说明关于伪t-模与蕴涵算子的文献FSS 132(2002)113]中定理4.1是错误的,此定理还被接连用到FSS 139(2003)673]及其它文献。本文进而给出此基础性定理成立的一个必要条件。注意,该必要条件是不能由无穷∨-分配伪t-模与无穷∧-分配蕴涵算子的定义引出的。
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| 关 键 词： | 非经典逻辑 伪t-模 蕴涵算子 |
| 文章编号： | 1001-7402（2006）01-0103-04 |
| 收稿时间： | 2004-10-11 |
| 修稿时间： | 2004年10月11 |
Note on "Pseudo-t-norms and implication operators on a complete Brouwerian lattice" |
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| HAN Song-chol,LI Hong-xing.Note on "Pseudo-t-norms and implication operators on a complete Brouwerian lattice"[J].Fuzzy Systems and Mathematics,2006,20(1):103-106. |
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| Authors: | HAN Song-chol LI Hong-xing |
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| Institution: | 1. Department of Mathematics and Mechanics,Kim I1 Sung University,Pyongyang,D. P. R. Korea; 2. School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China |
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| Abstract: | This paper shows by examples that Theorem 4.1 in Wang and Yu Fuzzy Sets and Systems 132 (2002)113], also used one after another in Fuzzy Sets and Systems 139(2003) 673] and other references, about pseudo-t-norms and implication operators is false. Furthermore, a necessary condition for this basic theorem to be true is presented. Note that the necessary condition does not follow from the definitions of infinitely ∨-distributive pseudo-t-norm and infinitely ∧-distributive implication. |
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| Keywords: | Non-classical logic Pseudo-t-norm Implication |
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