Eliminating redundant rules in a given system of fuzzy rules is an important step towards simplicity and clarity of the system. This presentation focuses on the generalization of the existing redundancy criteria for linguistic fuzzy rules using evaluative linguistic expressions. Then, a new algorithm for an automatic detection and deletion of redundant linguistic fuzzy rules is developed. Moreover, the consistency in deriving the redundancy or non-redundancy of a certain rule in a given system of fuzzy rules is addressed. The positive impact of this result can be seen in the efficient improvement of the developed algorithm, which helps to significantly decrease the running time of the algorithm.