This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a cha...This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.展开更多
It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular...It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular, it demonstrates several basic equivalent characterizations on the retriev-ability of (?) valued automata. Finally, the connections of the homomorphisms between two eeeeeeeeee valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.展开更多
基金This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004) the National Key Project for Basic Research (Grant No.1998030509) the National Natural Science Foundation of China (Grant No. 69823001).
文摘This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and par-ticularly presents a characterization of residuated lattice by fuzzy automata (called (?) valued automata). After that fuzzy subautomata (called (?) valued subautomata), successor and source operators are pro-posed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally an L bifuzzy topological characterization of Q valued automata is presented, so a more generalized fuzzy automata theory is built.
基金This work was supported by the National Foundation for Distinguished Young Scholars (Grant No. 69725004)the National Key Project for Basic Research (Grant No. 1998030509).
文摘It reveals some equivalences between automata based on complete residuated lattice-valued logic (called (?) valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular, it demonstrates several basic equivalent characterizations on the retriev-ability of (?) valued automata. Finally, the connections of the homomorphisms between two eeeeeeeeee valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.
基金The project TIN-2009-0828四川省中国关键技术研究和发展项目(Grant No.2011FZ0051)+5 种基金Wireless Administration of Ministry of Industry and Information Technology of China([2011]146)中国博士后科学基金资助项目(2013M540716)国家自然科学基金资助项目(Grant No.6087503461175055)陕西省自然科学基金资助项目(2012JQ1023)西安石油大学博士启动基金资助项目(2011BS017)