This paper shows how linguistic classification knowledge can be extracted from numerical data for pattern classification problems with many continuous attributes by genetic algorithms. Classification knowledge is extracted in the form of linguistic if-then rules. In this paper, emphasis is placed on the simplicity of the extracted knowledge. The simplicity is measured by two criteria: the number of extracted linguistic rules and the length of each rule (i.e., the number of antecedent conditions involved in each rule). The classification ability of extracted linguistic rules, which is measured by the classification rate on given training patterns, is also considered. Thus our task is formulated as a linguistic rule extraction problem with three objectives: to maximize the classification rate, to minimize the number of extracted linguistic rules, and to minimize the length of each rule. For tackling this problem, we propose a multi-objective genetics-based machine learning (GBML) algori...