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First, two new relations between knowledge structures are introduced through the use of their respective Boolean relation matrices, where the granular equality relation is defined based on an orthogonal transformation with the transformation matrix being a permutation matrix, and the granularly finer relation is presented by combining the classical finer relation and the orthogonal transformation. Then, it is demonstrated that the simplified knowledge structure base with the granularly finer relation is a partially ordered set, which can be represented by a Hasse diagram. Subsequently, an axiomatic definition of information granularity is proposed to satisfy the constraints regarding these two relations. Moreover, a general form of the information granularity is given, and some existing measures are proved to be its special cases. Finally, as an application of the proposed measure, the attribute significance measure is developed based on the information granularity.<\/jats:p>","DOI":"10.3233\/jifs-202086","type":"journal-article","created":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T15:05:55Z","timestamp":1622214355000},"page":"451-466","source":"Crossref","is-referenced-by-count":1,"title":["Transformations and information granularity of knowledge structures in\u00a0set-based granular computing"],"prefix":"10.1177","volume":"41","author":[{"given":"Wen Sheng","family":"Du","sequence":"first","affiliation":[{"name":"School of Business, Zhengzhou University, Zhengzhou, P.R. 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