The Application And Study Of Algorithm In Filtering, Interpolation And Approximation Based On Fuzzy Theory

Since American scientist L.A.Zadeh published famous thesis " Fuzzy Sets " in 1965, this is the marking of the birth of fuzzy mathematics. In a short period of 40 years, this theory has been developed rapidly, and has showed its strong application ability combining with new theory constantly. Fuzzy theory breaks through the limit of the classical two value theory , and widens " this or that " to " either-or " nature. The more important thing is that fuzzy theory provides one theory and method of the fuzzy message, and under the fuzzy inference and fuzzy subordination function, it can turn the theory and method into the things that machine can "understand" and accept. Through this bridge of fuzzy mathematics, it gets up fuzzy ration description of human thinking, and it can use computer to deal with mankind fuzzy experience, so it becomes the focal point that fifth generation of intelligent computer studies. This thesis discusses the technology of filtering ,interpolation and approximation based on fuzzy theory, and tries to incorporate fuzzy theory into the algorithm of traditional signal progressing. It makes the treatment of the algorithm not only on the mathematics descriptive ration of the sample data, but also on the combination of the fuzzy rule and fuzzy reasoning , so it introduces " intelligence " among them . In the field of filtering algorithm, this thesis introduces two filtering algorithms which are used for the singal that is polluted by the mixing of Gaussian noise and impulse noise. One kind takes the median output as the value of the membership function, and counts the weighted filter output. The other kind takes the mean output as the value of the membership function. Two algorithms breaks through the shortcoming of weighting value immobilizes in the traditional average filter algorithm, and it can characteristic adjust the weights from of data in the filter window, thus makes the weights from noise point is very small contributing to the output date. Through adjusting the filtering factor, it has good inhibition on pulse noise and gauss noise. This thesis makes some summaries to the performance of the two kinds of algorithms, and can draw the conclusion that within the range of certain precision, two kinds of algorithms can already not only strain the noise, but also protect the details of the signal to a certain extent, and has described the essence of fuzzy C-average that two kinds of algorithms reflect in thesis, thus describe the dependability of the algorithm. Apply fuzzy theory to the filter field, on the whole, it is a kind of non-linearly filter method. The tradition filter method only considers randomness. Fuzzy filter method considers not only randomness but also fuzzy character, so it is even more comprehensive. he fuzzy filtering theory is not complete perfect, and how to set up effective fuzzy rules, carry better fuzzy inferences based on counting, rationaly explain the change of frequencies, especially mixed frequency of the signal and noise, not only give consideration to the traditional minimum square criterion, but also make effective filter used fuzzy theories ,is a worth studying problem in the future. In the field of interpolation and approximation , the research of the fuzzy theory has very strong practicability, because the essence of fuzzy control is the fuzzy interpolation and the fuzzy approximation. This thesis discusses the general structure method of the fuzzy interpolation on the basis ofintroducing classics interpolation briefly. The traditional interpolation is often superposed from the formal weighting interpolation function. In the essence of fuzzy interpolation, its interpolation function is a group of " IF-THEN " fuzzy rules. And through the fuzzy subornation and fuzzy reasoning, it makes these rules have quantitative description method on mathematics. It is obvious that the fuzzy interpolation method not only uses the date information but also introduce human fuzzy thinking among them ,so it can improve the intelligent and precision of the interpolation. The thesis expounds the essence of using fuzzy triangle interpolation based on the classical interpolation. And discusses the relation of the fuzzy interpolation with the traditional interpolation in the one point fuzzy and T-S fuzzy output, states the inherent essential relation between fuzzy interpolation and traditional interpolation. Fuzzy approximation is a faster new developing direction in recent years. The thesis first recommends the famous fuzzy Gaussian approximation system which is based on the Gaussian membership function, the fuzzy logic of product reasoning and the fuzzy law of weight approach. This thesis is discusses the general fuzzy Gaussian membership function that can approximate the form of triangular, trapezoid and Gaussian function , and its basic form is μF ( x ) = exp ???? ?x ?abc???? .The general fuzzy Gaussian membership function is to be generally used in the field of approximation . The thesis proves the general fuzzy Gaussian approximation theory. Because other kind of membership function can obtain from adjusting the parameter of the general fuzzy Gaussian membership function, the general fuzzy Gaussian approximation theory shows that it is another...