Hedge algebras establish a sound approach (HA-approach) to the inherent semantics of words and provides a formalized basis to incorporate the fuzzy set based semantics of words with their own inherent semantics. On this basis, we are able to examine in the study a new concept of semantics-based interpretability of FRBSs and develop a genetic method to design interpretable FRBSs to solve regression problems, for instance. The proposed method is characterized by the following features: (i) The interpretability of FRBSs is guaranteed by the constraints proposed to preserve essential characteristics of the semantics of words that can be handled by only adjusting fuzziness parameters of variables; (ii) Each variable is associated with a word-set rich enough to be considered as a user word-vocabulary of the variable, called user’s Linguistic Frame of Cognitive (LFoC), which is properly represented by a multi-granularity structure; (iii) Large cardinalities of the LFoCs do not increase the method search space, despite of this the method can still decrease significantly the number of the initial rules, as they are generated from the patterns of the given datasets, exploiting the similarity-intervals of words; (iv) Concurrent learning rule bases and fuzziness parameters that determine the fuzzy set based semantics of the words of the given LFoCs; (v) The ability to reach a suitable trade-offs between the word generality and specificity and between the accuracy and the interpretability of the designed FRBSs. The proposed method is shown to statistically outperform the two counterpart methods examined by Alcalá et al. (2009), and Antonelli et al. (2011) and run over 9 and 6 regression datasets, respectively.