Quasi-linear fuzzy number and its application in fuzzy programming

System of fuzzy equations is a widespread problem in many applied fields such as production planning, resource management, optimization decision etc., and the variation description of fuzzy variables is the bottleneck problem of realizing solution operation. Starting from the structure feature of fuzzy information and the essential characteristic of fuzzy decision, this paper proposes the concept of quasi-linear fuzzy number, and discusses its operational characteristics and approximation properties, and establishes solution model based on metric and uncertainty restriction for system of fuzzy equations (denoted by FESM-M+U, for short); further, on the basis of quasi-linear fuzzy number and principal operation strategy, gives a genetic algorithm named by FGA-QL+PO; finally, considers its convergence using Markov chain theory and analyzes its performance through an example. All these indicate that, FGA-QL+PO can not only effectively reflect decision consciousness, but has good global convergence, and be suitable for all systems of fuzzy equations, so it can be widely used in many problems.