Fuzzy Reconstruction Based On Label Semantics And Prototype Theory

In the classic Cantor set theory,the relation between an object and a sample only have two kinds:belonging and not.This brings the convenience of calculation,but in reality many problems can't be described,Professor Zadeh's fuzzy set theory successfully solved this problem.But it needs to calculate the membership function.Membership function plays an import role in the fuzzy set theory.The classic methods for calculating membership function often need to specify a specific function to fit.It depends on the expert's experience.For this reason,we propose a fuzzy reconstruction method based on label semantics and prototype theory to determine the membership function of fuzzy sets.We first reconstruct each sample using the prototypes,and then we add the entropy penalty item to the reconstruction object function.The reconstruction coefficients are limited to the interval[0,1],and the sum of all the reconstruction coefficients is 1.The objective function is:argmin?x-WP?2/2 + APln(PT),s.t.?wi?1,Wi>0.The goal of the solution is to minimize the reconstruction error and maximize the entropy.The objective function ensures that the reconstruction error is as small as possible,and each point participates in the reconstruction process as much as possible.The addition of the coefficient constraint ensures that all coefficients are in the interval[0,1],making the reconstruction coefficients physically meaningful.The probabilistic quality function of the label can be obtained from the reconstruction coefficients.According to the probability quality function,the membership function can be obtained.Using the fuzzy reconstruction method based on label semantics and prototype theory to obtain the membership function.the membership function has three properties:context dependency,semantic reconstruction,and ordering preserving.The classification experiments of fuzzy reconstruction on handwritten numerals,human faces,sonar signals and other data sets show that the results of Classification Algorithm Based on Fuzzy Reconstruction(FRC)are robust compared with the traditional algorithms,and are not sensitive to different data distributions.The effect can reach the most advanced level.It can be proved that the fuzzy reconstruction method based on label semantics and prototype theory can get the distribution of membership function which is consistent with the actual data.