||This contribution is concerned with the interpretability of fuzzy rule-based systems. While this propertyis widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what"interpretability" actually means is not available. So far, interpretability has most often been associated withrather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, weattempt to approach this problem from a more general and formal point of view. First, we clarify what the differentaspects of interpretability are in our opinion. Consequently, we propose an axiomatic framework for dealing with theinterpretability of linguistic variables (in Zadeh's original sense) which is underlined by examples and applicationaspects, such as, fuzzy systems design aid, data-driven learning and tuning, and rule base simplification.