Fuzzy Implication Operators And Applicability On Fuzzy Control Systems

The construction on fuzzy implication operators(briefly written as FIOs), the sufficient conditions and the necessary conditions on which fuzzy controllers are universal approxi-mators respectively, and applicability on fuzzy control systems are researched in detail. The main results are as follows :1. The construction on FIOs are considered in chapter 3. The concepts of rule-union operators and the rule-intersection operators are introduced for the first time. 412 FIOs are given, thereinto,353 FIOs are constructed by us and 59 FIOs appear in some references. Besides, 2 kinds of methods in order to construct FIOs are introduced.2. 2 sufficient conditions and 2 necessary conditions are respectively given on which fuzzy controllers are universal approximators in chapter 4. Firstly, the interpolation merch-anism of fuzzy controllors are discussed,then 4 classes of fuzzy controllers are classified by their applicability.3.The applicability on fuzzy control systems are investigated in chapter 5. The concept of the choice mechanism are introduced for the first time. Fuzzy controllers based on the choice mechanism are called as self-adaptive fuzzy controllers. 127 fuzzy controllers are universal approximators,in the meaning of equivalent, they can be classified 44 kinds of fuzzy controllers,thereinto, 17 fuzzy controllers are self-adaptive fuzzy controllers. Therefore, they must be universal approximators and of course can be used in practical fuzzy control systems.4. We name a class of fuzzy controllers as ambiquity including ambiquity I and ambiq-uity II.