报告题目：Approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures
报告人： 李永明 教授 陕西师范大学
主持人： 陈仪香 教授
报告时间：10月12日 周五15:00-17:00
报告地点：数学馆201报告厅
报告人简介：
陕西师范大学计算机科学教授，博士生导师。主要研究方向：非经典计算理论、量子计算与量子信息、定量模型检测、计算智能、模糊系统分析、格上拓扑学。2001年国务院政府特殊津贴获得者，曾获得2002教育部第三届“高校青年教师奖”（教育部高层次人才奖励计划）。先后在清华大学、加拿大Alberta大学、澳大利亚悉尼科技大学、德国莱比锡大学、美国肯塔基大学等校访问和合作研究。担任国际IEEE计算智能模糊系统技术委员会委员、全国运筹学会智能计算学会副理事长、全国高等师范学校计算机教育委员会副理事长、中国系统工程学会模糊数学与模糊系统委员会副理事长、中国计算机学会理论计算机学会理事等职。曾任多个国际会议的大会主席、程序委员会主席、组织委员会主席，以及委员，并多次做特邀大会报告。在科学出版社出版专著两部，在《SCI》源期刊发表论文100余篇。
报告摘要：
For the purpose of reducing the number of states of fuzzy automata, we study approximate bisimulations of fuzzy automata under fuzzy similarity measures, which are induced by residuums of left-continuous t-norms. For a real number $/alpha/in [0,1]$ and a fuzzy similarity measure $S$, we define $/alpha$-approximate bisimulation under $S$ between two fuzzy automata and prove that the degree of similarity between them is more than or equal to $/alpha$ if there exists an $/alpha$-approximate bisimulation between them. Furthermore, we put forward the notion of surjective functional $/alpha$-approximate bisimulations between two fuzzy automata under $S$. Using the notion of surjective functional $/alpha$-approximate bisimulations under $S$, the $/alpha$-approximate bisimulations for a fuzzy automaton under $S$ is defined as an equivalence relation with two additional properties. According to an $/alpha$-approximate bisimulation for a fuzzy automaton, an aggregated fuzzy automaton has been constructed and the degree of similarity between them is also more than or equal to $/alpha$. It is significant for us to find that there might not possess the greatest $/alpha$-approximate bisimulation for a fuzzy automaton, and we provide a polynomial-time algorithm for computing all maximal $/alpha$-approximate bisimulations. Finally, we provide the conditions of the existence of the greatest $/alpha$-approximate bisimulation.
