A Study On The Iterative Solution Of A System Of Fuzzy Linear Equations

The study of the solutions to the fuzzy linear equations constitutes an important part of fuzzy algebra. And this thesis takes the study of solutions to a type of fuzzy linear equation set in the form of X=AX+U and the iterate algorithm as the central issue. In this form of equation the unknown quantity X and constant U are both vectors made up of fuzzy numbers, while A may exist in three states: (i) n×n real number matrix and the study of this state constitutes the second chapter; (ii) n×n interval number matrix (i. e. the matrix made up of interval number elements )and the study of this state constitutes the third chapter; (iii) nxn fuzzy number matrix (i. e. the matrix made up of fuzzy number elements) and the study of this state is the subject of the fourth chapter. The subjects of each chapter bear a similarity in two points: (i) the condition in which the equation set has solutions; (ii) when the former condition is fulfilled the iterative algorithm of the equation set and the estimation of its errors. The addition, multiplication and shucheng in this thesis are all defined according to the expansion theory of Zadeh.