| 完备格上模糊关系方程的研究进展 |
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| 引用本文： | 王学平. 完备格上模糊关系方程的研究进展[J]. 四川师范大学学报(自然科学版), 2009, 32(3). DOI: 10.3969/j.issn.1001-8395.2009.03.023 |
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| 作者姓名： | 王学平 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 摘 要： | 从理论研究的角度总结了模糊关系方程30余年来的研究进展,内容包括:完备Brouwer格上sup-inf合成模糊关系方程的极小解及方程的解集,其中包括论域有限时完备Brouwer格上模糊关系方程的极小解及方程的解集以及论域无限时完备Brouwer格上模糊关系方程的极小解及方程的解集;完备Brouwer格上inf-α合成模糊关系方程的极大解及方程的解集;格上元素的分解与模糊关系方程的极小(大)解的关系;最后,介绍了MV-代数上的半线性空间及定义在其上的模糊关系方程.
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| 关 键 词： | 完备格 模糊关系方程 极小解 极大解 半线性空间 解集 |
The Advance of Reseach on Fuzzy Relational Equations on Complete Lattices |
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| WANG Xue-ping. The Advance of Reseach on Fuzzy Relational Equations on Complete Lattices[J]. Journal of Sichuan Normal University(Natural Science), 2009, 32(3). DOI: 10.3969/j.issn.1001-8395.2009.03.023 |
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| Authors: | WANG Xue-ping |
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| Affiliation: | College of Mathematics and Software Science;Sichuan Normal University;Chengdu 610066;Sichuan |
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| Abstract: | This paper summarizies the advance of reseach on fuzzy relational equations on complete lattices in the past thirty years from the viewpoint of theory.Its content consists of four parts:the first one is minimal solutions of fuzzy relational equations with sup-inf composition and their solution sets on complete Brouwerian lattices,which includes both minimal solutions of finite fuzzy relational equations and their solution sets,and minimal solutions of infinite fuzzy relational equations and their solution s... |
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| Keywords: | Complete lattice Fuzzy relational equation Minimal solution Maximal solution Semilinear space Solution set |
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