This paper aims at identifying the factors that would help to diagnose acute myocardial infarction (AMI) using data from an electronic medical record system (EMR) and then generating structure decisions in the form of linguistic fuzzy rules to help predict and understand the outcome of the diagnosis. Since there is a tradeoff in the fuzzy system between the accuracy which measures the capability of the system to predict the diagnosis of AMI and transparency which reflects its ability to describe the symptoms-diagnosis relation in an understandable way, the proposed fuzzy rules are designed in a such a way to find an appropriate balance between these two conflicting modeling objectives using multi-objective genetic algorithms. The main advantage of the generated linguistic fuzzy rules is their ability to describe the relation between the symptoms and the outcome of the diagnosis in an understandable way, close to human thinking and this feature may help doctors to understand the decision process of the fuzzy rules.