{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:18:50Z","timestamp":1777706330177,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,8,10]]},"abstract":"<jats:p>The uncertainty of information plays an important role in practical applications. Uncertainty measurement (UM) can help us in disclosing the substantive characteristics of information. Probabilistic set-valued data is an important class of data in machine learning. UM for probabilistic set-valued data is worth studying. This paper measures the uncertainty of a probability set-valued information system (PSVIS) by means of its information structures based on Gaussian kernel method. According to Bhattacharyya distance, the distance between objects in each subsystem of a PSVIS is first built. Then, the fuzzy Tcos-equivalence relations in a PSVIS by using Gaussian kernel method are obtained. Next, information structures in a PSVIS are defined. Moreover, dependence between information structures is investigated by using the inclusion degree. As an application for the information structures, UM in a PSVIS is investigated. Finally, to evaluate the performance of the investigated measures, effectiveness analysis is performed from dispersion analysis, correlation analysis, and analysis of variance and post-hoc test.<\/jats:p>","DOI":"10.3233\/jifs-210460","type":"journal-article","created":{"date-parts":[[2022,6,7]],"date-time":"2022-06-07T12:33:14Z","timestamp":1654605194000},"page":"4645-4668","source":"Crossref","is-referenced-by-count":0,"title":["Uncertainty measurement for probabilistic set-valued data: Gaussian kernel method"],"prefix":"10.1177","volume":"43","author":[{"given":"Wenwu","family":"Lian","sequence":"first","affiliation":[{"name":"School of Physics and Telecommunication Engineering, Yulin Normal University, Yulin, Guangxi, P.R. 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