Study On The Weight Sensitive Analysis In Fuzzy Decision Making And Their Applications

System fuzzy decision and neural network are the current research fields for system science. Firstly, this paper reviews the history of fuzzy decision-making, summarizes the current situation of multi-objective fuzzy decision and neural network. By using the method of perturbation analysis, the weight sensitive analysis of fuzzy decision is studied in those respects: Multi-objective fuzzy optimization, fuzzy pattern recognition, fuzzy classification, and fuzzy dynamic programming with multi-objectives. Two fuzzy neural networks are studied. One is about fuzzy optimization; the other is about fuzzy recognization. The main contents and results are listed as follows1. Based on the model of multi-objective fuzzy optimization, the sensitivity of fuzzy optimization about weight perturbation is discussed. A transfer equation is presented. An universal up-bound of transfer matrix is given. A global estimate in-equation is performed. Two conditions are introduced. One can preserve the order of decision membership degree series; The other can preserve stability. In accordance with preserve the order problem of multi-objective fuzzy optimization; two weight perturbation conditions are suggested. One can preserve order condition in membership series of decision; the other can exchange the order. In order to solve the inverse problem of multi-objective fuzzy optimal selection, two methods are suggested by using the model of multi-objective optimal selection. One is a linear equation system; other is a 2-order mathematical programming. The sensitive analysis of decision membership degree is made by means of the model of the cross iteration. A second decision method suggested by Professor Chen is introduced. Some examples aboutdesign of hydroelectric engineering, flood-control operation, ocean platform design testify the above conclusions.2. Based on the model of fuzzy patter recognition, the weight perturbation transfer equation of recognizes matrix is presented. A modified formula of criticize index grade is put forward. The weight perturbation of fuzzy classification is discussed. Two important formulas are introduced. One is the weight perturbation formula of classifiable matrix, other of center matrix. In accordance with multi-objective fuzzy dynamic programming, the stage formulas with weight perturbation are suggested. An example of water resource planning is given.3. The algorithm of fuzzy neural network is studied; a concept of equal effective error function is suggested. An algorithm is given based on the Hessian matrix of error function; this calculating method is more effective than the grandaunt algorithm, which has meaning of batched presses.4. By using the homotopy method of fuzzy neural net-work for solving the system of nonlinear equations, a homotopy method is suggested in the fuzzy optimal neural net-work. The calculation of fuzzy optimal neural network can turn to a boundary problem of differential equation, and then be solved by using Euler or Runge-Kutta methods, which has the property of finite convergence.Finally, a summary is made and some problems to be further studied are discussed.