WordNet-like Lexical Databases (WLDs) group English words into synsets, being utilized in several text mining applications. Synsets were also open to criticism, because while synset members (wordsenses) are, in practice, considered as compeers, yet in theory not all of them represent the synset meaning with a same degree. Considering this criticism, fuzzy synsets (considering synsets as fuzzy sets) have been proposed. In this study, we show why the standard fuzzy synsets do not properly-enough model the membership uncertainty, and propose an upgraded version of them in which membership degrees are represented by intervals (similar to what in Interval Type 2 Fuzzy Sets). We present an algorithm for constructing the interval fuzzy version of WLDs of a language, given a large enough multi-contextual corpus of documents and a precise enough word-sense-disambiguation (WSD) system of that language. Utilizing the algorithm, we produced interval fuzzy synsets of English WordNet (for the frequent-enough synsets). For evaluation, we compared the results with crowdsourced data, asking people to rate the min/max compatibility degree of wordsenses of a synset with its definition. Comparisons, promisingly, showed the algorithm accuracy. The algorithm has also the drawback of being applicable only for synsets with wordsenses having enough frequency in all the corpus categories. This drawback is going to be covered in our future work.