In this paper we propose a multi-objective evolutionary algorithm with a mechanism to improve the interpretability in the sense of complexity for Linguistic Fuzzy Rule based Systems with adaptive defuzzification. The use of parameters in the defuzzification operator introduces a series of values or associated weights to each rule, which improves the accuracy but increases the system complexity and therefore has an effect on the system interpretability. To this end, we use maximizing the accuracy as an usual objective for the evolutionary process, and we define objectives related with interpretability, using three metrics: minimizing the classical number of rules, the number of rules with weights associated and the average number of rules triggered by each example. The proposed method was compared in an experimental study with a single objective accuracy-guided algorithm in two real problems showing that many solutions in the Pareto front dominate those obtained by the single objective-based one.