A funtadamental study on graph transforamtion systems with relational calculus

本研究项目获得了以下结果：·我们开发了一个模糊关系代数的轴向形式，作为模糊关系计算的基础。通过使用公式化我们对关系代数的表示问题进行概括，对A.Tarski进行概括，对Dedekind和Zadeh类别的表示问题，我们对Dedekind和Zadeh类别的表示问题提供了证据。我们提出了一种基于模糊关系计算理论的模糊图形转换的新方法。然后，我们在模糊图形类别中提供了推回的存在，是哪一个Gurantees为推回图形转换奠定了基础。我们发明了一个关系集理论，作为图形转换的重要基础，作为数学和理论计算机科学。此外，我们还从一个非常宽的角度对它的应用进行了调查。本研究项目摘要的详细内容是在《研究项目报告》（小册子）中描述的，印刷在九州大学信息学系。首席调查员，在项目调查员的一半以上，感谢为项目提供财务支持。

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.