| 基于一类完备格诱导的直觉模糊集的多元扩展运算 |
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| 引用本文： | 宋巍巍,王贵君.基于一类完备格诱导的直觉模糊集的多元扩展运算[J].天津师范大学学报(自然科学版),2014(3):7-10. |
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| 作者姓名： | 宋巍巍 王贵君 |
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| 作者单位： | 天津师范大学数学科学学院,天津300387 |
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| 基金项目： | 国家自然科学基金资助项目（61374009） |
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| 摘 要： | 基于一种二元序完备格引入了直觉模糊集的截集的概念,给出了直觉模糊集的加、减和乘法等算术运算,获得了这种截集的算术运算性质,并通过实例说明这些包含关系可以严格成立.此外,在完备格诱导的直觉模糊集的截集基础上,得到了直觉模糊集的多元扩展原理,进而讨论了多元扩展运算的2个基本性质.
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| 关 键 词： | 直觉模糊集 完备格 算术运算 多元扩展原理 |
Multivariate extension operations of intuitionistic fuzzy sets induced by a complete lattice |
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| SONG Weiwei,WANG Guijun.Multivariate extension operations of intuitionistic fuzzy sets induced by a complete lattice[J].Journal of Tianjin Normal University(Natural Science Edition),2014(3):7-10. |
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| Authors: | SONG Weiwei WANG Guijun |
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| Affiliation: | (College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China) |
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| Abstract: | The concept of cut set of intuitionistic fuzzy set is introduced based on the complete lattice of a kind of binary order. The arithmetic operations of intuitionistic fuzzy sets such as addition, subtraction and multiplication are given, some properties of the arithmetic operation of the cut sets are obtained. An example shows that the strict inclusion relations of the cut sets are possible to sure. In addition, on the basis of the cut sets induced by a complete lattice, the multivariate extension principle of intuitionistic fuzzy sets is gained, and then the two basic properties of the multivariate extension operation are discussed. |
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| Keywords: | intuitionistic fuzzy sets complete lattice arithmetic operation multivariate extension principle |
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