From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction pr...From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.展开更多
Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoni...Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.展开更多
基金supported by the National Natural Science Foundation of China (61105076 61070124)+2 种基金the National High Technology Research and Development Program of China (863 Program) (2012AA011103)the Open Project of State Key Laboratory of Virtual Reality Technology and Systems of China (BUAA-VR-10KF-5)the Fundamental Research Funds for the Central Universities (2011HGZY0004)
文摘From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.
文摘Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.
