Fuzzy Support Vector Machines And Its Application

Support vector machines (SVMs), which was proposed by Vapnik and etc, is one of the standard tools for machine learning and data mining. It can deal with classification problems and regression problems successfully. Because of its excellent learning power, this technology has been the topic of machine learning. But as a new technology, it still has some problems. There are lots of fuzzy information in the objective world, and if the training set has fuzzy information (fuzzy parameters) in SVMs, traditional SVMs will fail.This paper researches on the construction problem of fuzzy SVMs when the output of training point is triangle fuzzy number.Including the following parts:1. Research on the fuzzy SVMs based on possibility theory. Propose the definitions of possibility measure, fuzzy number, triangle fuzzy number, introducing the model and algorithm of fuzzy chance constrained programming. On this base, construct fuzzy support vector classification (Algorithm) from three aspects (fuzzy linearly classification problem, nearly fuzzy linearly classification problem and fuzzy nonlinearly classification problem). We also do some research on the method of computing optimal confidence level.2. Research on the fuzzy SVMs based on fuzzy coefficient programming. Proposed the definitions of level cut set of fuzzy number, maximum (minimum) of fuzzy parameter function, introduced the model and algorithm of fuzzy parameter programming. And on this base, constructing fuzzy support vector classification (Algorithm) from three aspects (linearly classification problem and nonlinearly classification problem). This part also did some research on the method of computing optimal bias.3. This part constructed fuzzy linear support vector regression when the parameters of optimal hyperplane are fuzzy (fuzzy vector or fuzzy number). Proposed the model of fuzzy chance constrained programming with fuzzy decision, and did some research on fuzzy linear support vector regression(algorithm) on this base. Furthermore for the above model, discussed its solving method — the generic algorithm based on fuzzy simulation, and also gave out the definition of fuzzy support vector set(fuzzy set).4. Apply fuzzy support vector classification to the coronary heart diagnose and the city air quality assessment, and derive new methods of diagnosing and assessing — the fuzzy support vector classification.