Finding sequential patterns is one of important issues in data mining. This paper deals with linguistic (fuzzy) sequential patterns. The existing algorithms for discovering such patterns do involve usual sigma counts of fuzzy sets as measure of support. Unfortunately, a well-known side effect is then an undesirable cumulation of small membership values. We like to propose an improved approach based on generalized sigma counts, which in particular leads to a consequently lower cumulation, and considerably to better results. We test the modified algorithm using different generalized sigma counts based on different cardinality pattern functions.