In fact, FSI and ASI always provide an interpretation of W. While FSI includes in I the sense having minimal cumulated distance to the first senses of the rest of words in W, ASI includes in I the sense having minimal cumulated distance to the all the senses of the rest of words in W. The rationale behind the FSI algorithm is that the most frequent sense for a word, according to the WN sense ranking is very competitive in WSD tasks, and it is extremely hard to improve upon even slightly [18].
this algorithm expects that the first sense in WN will be correct for most of the words in W. Regarding ASI, this algorithm expects that the words in W (corresponding to a very close semantic field) will establish many close path connections between different synsets of the same word (because of the fine-grained sense distinction of WN).