Method for Solving a System of Fuzzy Equations Based on Metric and Allowable Uncertainty

System of fuzzy equations is a widespread problem in many applied fields such as resource management, production planning, optimization decision and artificial intelligence, in which, establishing general and operable solving methods has received a remarkable attention in academic circles. In this paper, using the structure feature of fuzzy number, we propose the concept of level effect function which can describe fuzziness consciousness, and establish a broad operable fuzzy metric based on level effect function; on the basis of essential characteristic of fuzzy decision, establish solution model based on metric and uncertainty restriction for system of fuzzy equations (denoted by MEBU- FESM, for short); combining genetic algorithm and variance description strategy of principle index of fuzzy variable, give solution method based on genetic algorithm (denoted by PO-FGA, for short); finally, consider its convergence using Markov chain theory and analyze its performance through simulation.