In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the s...In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc, are given. Those distributions act as ＂inner kernels＂ of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways： 1） Two methods are equivalent; 2） the latter is a degeneration of the former; 3） the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.展开更多
Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shape...Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shapes of membership functions are important, because it has an effect on fuzzy inference system. The shapes of membership functions can be triangular, trapezoidal and gaussian. The most widely used triangular membership function is used in this paper, because it can capture the short time period. In washing machine, open loop control system is found. This paper applies a fuzzy synthetic evaluation method (FSEM) for washing cloth in washing machine as FSEM can handle the multiple criteria with the help of evaluation matrix generated from membership function and weight matrix generated by Analytical Hierarchy Process (AHP). The purpose of this research is to minimize the wash time. By applying FSEM, we get a wash time which is less than that wash time got from applying the Mamdani approach in FCS. An example is given for illustration. For more reduction of wash time, statistical averaging method is also used. To reduce the wash time, statistical averaging method can be used in Mamdani approach also.展开更多
Development of accurate and reliable models for predicting the strength of rocks and rock masses is one of the most common interests of geologists,civil and mining engineers and many others.Due to uncertainties in eva...Development of accurate and reliable models for predicting the strength of rocks and rock masses is one of the most common interests of geologists,civil and mining engineers and many others.Due to uncertainties in evaluation of effective parameters and also complicated nature of geological materials,it is difficult to estimate the strength precisely using theoretical approaches.On the other hand,intelligent approaches have attracted much attention as novel and effective tools of solving complicated problems in engineering practice over the past decades.In this paper,a new method is proposed for mining descriptive Mamdani fuzzy inference systems to predict the strength of intact rocks and anisotropic rock masses containing well-defined through-going joint.The proposed method initially employs a genetic algorithm(GA)to pick important rules from a preliminary rule base produced by grid partitioning and,subsequently,selected rules are given weights using the GA.Moreover,an information criterion is used during the first phase to optimize the models in terms of accuracy and complexity.The proposed hybrid method can be considered as a robust optimization task which produces promising results compared with previous approaches.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.60474023).
文摘In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc, are given. Those distributions act as ＂inner kernels＂ of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways： 1） Two methods are equivalent; 2） the latter is a degeneration of the former; 3） the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.
文摘Generally fuzzy control system (FCS) is worked in washing machine. For the fuzzy set theory, membership functions are the building blocks. In a fuzzy set, fuzziness is determined by its membership functions. The shapes of membership functions are important, because it has an effect on fuzzy inference system. The shapes of membership functions can be triangular, trapezoidal and gaussian. The most widely used triangular membership function is used in this paper, because it can capture the short time period. In washing machine, open loop control system is found. This paper applies a fuzzy synthetic evaluation method (FSEM) for washing cloth in washing machine as FSEM can handle the multiple criteria with the help of evaluation matrix generated from membership function and weight matrix generated by Analytical Hierarchy Process (AHP). The purpose of this research is to minimize the wash time. By applying FSEM, we get a wash time which is less than that wash time got from applying the Mamdani approach in FCS. An example is given for illustration. For more reduction of wash time, statistical averaging method is also used. To reduce the wash time, statistical averaging method can be used in Mamdani approach also.
文摘Development of accurate and reliable models for predicting the strength of rocks and rock masses is one of the most common interests of geologists,civil and mining engineers and many others.Due to uncertainties in evaluation of effective parameters and also complicated nature of geological materials,it is difficult to estimate the strength precisely using theoretical approaches.On the other hand,intelligent approaches have attracted much attention as novel and effective tools of solving complicated problems in engineering practice over the past decades.In this paper,a new method is proposed for mining descriptive Mamdani fuzzy inference systems to predict the strength of intact rocks and anisotropic rock masses containing well-defined through-going joint.The proposed method initially employs a genetic algorithm(GA)to pick important rules from a preliminary rule base produced by grid partitioning and,subsequently,selected rules are given weights using the GA.Moreover,an information criterion is used during the first phase to optimize the models in terms of accuracy and complexity.The proposed hybrid method can be considered as a robust optimization task which produces promising results compared with previous approaches.
