{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T15:25:18Z","timestamp":1770045918249,"version":"3.49.0"},"reference-count":41,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,12,16]]},"abstract":"<jats:p>An information system (IS), an important model in the field of artificial intelligence, takes information structure as the basic structure. A fuzzy probabilistic information system (FPIS) is the combination of some fuzzy relations in the same universe that satisfy probability distribution. A FPIS as an IS with fuzzy relations includes three types of uncertainties (i.e., roughness, fuzziness and probability). This paper studies information structures in a FPIS from the perspective of granular computing (GrC). Firstly, two types of information structures in a FPIS are defined by set vectors. Then, equality, dependence and independence between information structures in a FPIS are proposed, and they are depicted by means of the inclusion degree. Next, information distance between information structures in a FPIS is presented. Finally, entropy measurement for a FPIS is investigated based on the proposed information structures. These results may be helpful for understanding the nature of structures and uncertainty in a FPIS.<\/jats:p>","DOI":"10.3233\/jifs-210149","type":"journal-article","created":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T11:32:45Z","timestamp":1637926365000},"page":"6343-6361","source":"Crossref","is-referenced-by-count":0,"title":["Information structures and entropy measurement for a fuzzy probabilistic information system"],"prefix":"10.1177","volume":"41","author":[{"given":"Yanling","family":"He","sequence":"first","affiliation":[{"name":"Department of Business Administration, Baise University, Baise, Guangxi, P.R.\u00a0China"}]},{"given":"Chunji","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Finance, Baise University, Baise, Guangxi, P.R.China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-210149_ref1","first-page":"15","article-title":"Information entropy and granulationco-entropy of partitions and coverings: a 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