Research On The Granulation SVM Model Based On Intuitionistic Fuzzy Sets

Fuzzy set theory, proposed by Zadeh in 1965, is a mathematical tool to deal with uncertain knowledge. It can deal with the imprecise, inconsistent and incomplete information. It has been widely used and achieved harvest results in many fields. Such as, knowledge acquisition, expert systems, machine learning, granular computing and so on. Intuitionistic fuzzy sets theory was introduced by Atanassov as an intuitively straightforward extension of fuzzy set theory. By adding a non-membership function in the fuzzy set, it could reflect the fuzzy nature of the objective world, and attracted of many scholars paied the attention to the research about the intuitionistic fuzzy sets theory. As it plays a key role in the fields of machine learning, decision-making and classification researchs. Therefore, it is necessary to make further research about intuitionistic fuzzy sets theory in the application of machine learning.Support vector machine was proposed by Corinna Cortes and Vapnik in 1995, which solved the problem of machine learning classification and regression. Because SVM has the characteristics of complete basic theory, global optimization, short training time and strong generalization performance. And it has been a universally accepted and researched method of machine learning. American scholars Lin proposed the Granular computing in 1997. The basic idea of the theory of granular computing is divided the class of objects into many pieces. By the not clear relation, similarity relation, neighboring relation and so on. In the end we can have the futher graining.Therefore, based on the theory of intuitionistic fuzzy sets, granular computing, and support vector machines, we have research about the granularity support vector machine based on the intuitionistic fuzzy sets. The innovation points are as follows:(1) Reviewing the basic theory of intuitionistic fuzzy sets, we discuss the nature of intuitionistic fuzzy sets, and define a new precise function of interval-valued intuitionistic fuzzy sets. Using examples to illustrate the validity of new precise function, it applies to decision-making and classification problems.(2) Based on the basic theory of intuitionistic fuzzy sets, combining granular computing theory, we propose two types of the GSVM model based on intuitionistic fuzzy sets(GSVM-Ⅰ and GSVM-Ⅱ), and give the algorithms and its steps, finally through examples of simulation to verify their validity.The study provides a new method for intuitionistic fuzzy set and as a new classification for the model of support vector machines. It has important theoretical value. It provides new idea for classification and uncertain decision information systems.