Pseudo-additive Measure And Pseudo Integral Theory And Its Application In The Classifier

In this thesis, on the basis of basic theory and the latest research results of the existing fuzzy measure, pseudo-additive measure and pseudo-integrals theory based on pseudo-operator and its application in the system is discussed. The specific contents are revealed as follows:(1) Some important properties of pseudo-additive measures are discussed, such as continuity from above and continuity from below. The correlation between the measurable sets is given out with respect to a pseudo-additive measure and the corresponding pseudo-integrals of measurable function on them. And based on pseudo-additive measure, the classical Radon-Nikodym theorem is generalized to the pseudo-integrals theory.(2) Based on a continuous pseudo-addition, some properties of the upper-closures of the regular sub-spaces of the nonlinear functional space are discussed. The necessary and sufficient condition of a subset K of the nonlinear functional space F(X) is given out based on a strict pseudo-addition is an upper-complete normal subspace.(3) Some properties of the sequence of a.e. convergence and convergence in pseudo-additive measure are discussed. On the measurable functional spaces based on a strict pseudo-addition, the relationship between a.e. convergence and convergence in pseudo-additive measure is discussed, and necessary and sufficient conditions that a measurable functional sequence{fn}n>1is a.e. convergence in0on X are given out.(4) Based on pseudo-additive measures, two classes pseudo-integral classifier i.e., elementary pseudo-integral classifier and improve pseudo-integral classifier, are given out and applied the pseudo-integral based on pseudo-additive measures to the classifier fusion.