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Different approximations are also introduced. Furthermore, diverse coverings are also suggested.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>A tolerance class of an object is proved to be the join of semi\u2010equivalence classes containing it, i.e. a result of acting union operation on some primitive classes. A compatibly kernel class of an object is a meet of semi\u2010equivalence classes including it, i.e. a result of acting intersection operation on some primitive classes. Related coverings can also be regarded as coverings derived from the covering consisting of primitive granules. Several necessary and\/or sufficient conditions for a general covering to become a semi\u2010equivalence or complete covering are obtained. Meaningful property and relationship results are also exploited.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>Constructing diverse granules naturally from an incomplete information system to form a different knowledge expression system looks promising for data mining in the information society. It widens the approach and schema.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper shows that the formation process of granules is natural, newly defined, and not similar and theoretic to those existing in a neighborhood system. The relationship between diverse granules and coverings is described by mathematical theorems in sufficient or necessary condition form.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920810876945","type":"journal-article","created":{"date-parts":[[2008,6,14]],"date-time":"2008-06-14T07:02:36Z","timestamp":1213426956000},"page":"739-748","source":"Crossref","is-referenced-by-count":1,"title":["On blocks and coverings based on semi\u2010equivalence relation in pansystems methodology"],"prefix":"10.1108","volume":"37","author":[{"given":"Chen","family":"Wu","sequence":"first","affiliation":[]},{"given":"Xiaohua","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Jingyu","family":"Yang","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022030820032835100_b1","doi-asserted-by":"crossref","unstructured":"Bartol, W., Mir\u00f3, J., Pi\u00f3ro, K. and Rossell\u00f3, F. 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