A funtadamental study on graph transforamtion systems with relational calculus

基于关系演算的图变换系统的基础研究

• 批准号: 07680363
• 负责人: KAWAHARA Yasuo
• 金额: $ 1.47万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07680363/
• 关键词: graph transformation; graph grammar; relational calculus; relation algebra; category theory; fuzzy set; fuzzy relation; fuzzy graph; 関係代数; ファジィ集合; ファジィ関係; ファジィグラフ

This reseach project obtained the following results :・We developed an axiomatic formalisation of fuzzy relation algebras as a foundation of fuzzy relational calculus. By using the formalisation we generalized the representation problem for relation algebras, due to A.Tarski, to a representation problem for Dedekind and Zadeh categories, and we gave proofs of the representation problem for Dedekind and Zadeh categories.・We proposed a new matching method for fuzzy graphs in a theory of fuzzy graph transformations based on fuzzy relational calculus. Then we proved the existence of pullbacks in a category of fuzzy graphs, which gurantees the foundation for pullback graph transformations.・We invented relational set theory as an important foundation for graph transformations as well as mathematics and theoretical computer science. Also, we investigated its applications from a quite wide view.・The detailed summary of this reseach project is described in the report of the reseach project (booklet), printed in Department of Informatics, Kyushu University. The head investigator, on behalf of investigators of the project, is grateful for giving the financial suport.

该研究项目获得了以下成果：·我们开发了模糊关系代数的公理形式化，作为模糊关系微积分的基础。通过使用形式化，我们将关系代数的表示问题推广到 A.Tarski 的表示问题。 Dedekind和Zadeh范畴，并给出了Dedekind和Zadeh范畴的表示问题的证明。・我们在模糊图理论中提出了一种新的模糊图匹配方法然后我们证明了模糊图范畴中回退的存在性，这为回退图变换奠定了基础。 ・我们发明了关系集合论作为图变换以及数学和理论计算机的重要基础。此外，我们还从相当广泛的角度对其应用进行了研究。・本研究项目的详细摘要在九州信息学部印刷的研究项目报告（小册子）中进行了描述。首席研究员代表该项目的研究人员对给予的财政支持表示感谢。

项目成果

S.Inokuchi, T.Sato, A.hara, S.Kumamoto, H.-Y.Lee and Y.Kawahara: "Computational analysis of cellular automata with triplet transition rule." Research Report on Information Science and Electical Engineering of Kyushu University. 1(1). 79-84 (1996)

S.Inokuchi、T.Sato、A.hara、S.Kumamoto、H.-Y.Lee 和 Y.Kawahara：“具有三重态转移规则的元胞自动机的计算分析。”

S.Inokuchi: "Computational analysis of cellular automata with triplet transition rule" Research Report on Info.Sci.and Elect.Eng.of Kyushu University. 28. 79-84 (1996)

S.Inokuchi：“具有三重态转移规则的元胞自动机的计算分析”九州大学Info.Sci.and Elect.Eng.的研究报告。

Y.Kawahara: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

Y.Kawahara：“模糊关系的代数形式化”发表在《国际模糊集与系统杂志》上。

Y.Kawahara and H.Furusawa: "Crispness and representation theorem in Dedekind categories." DOI Technical Report DOI-TR-CS 143, Department of Informatics, Kyushu University.

Y.Kawahara 和 H.Furusawa：“Dedekind 范畴中的清晰度和表示定理”。

Y.Kawahara: "Period lengths of cellular automata cam-90 with memory" Journal of Mathematical Physics. 38. 255-266 (1997)

Y.Kawahara：“带记忆的元胞自动机 cam-90 的周期长度”《数学物理杂志》。