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In this paper, we try to develop a general framework of information measures and a flexible multiple attribute decision-making (MADM) approach in the interval type-2 fuzzy information environment. First, we propose the fuzzy factor, hesitant factor and interval factor to quantify the fuzziness, hesitancy and interval information of one IT2FS, respectively. An interval type-2 fuzzy cross-entropy has been initiated based on these three factors to measure the discrimination degree of uncertain information between two IT2FSs. Meanwhile, we exploit the axiomatic principles of interval type-2 fuzzy entropy and study the inherent relationship between cross-entropy and entropy measures. Then, some parameterized information measures are naturally investigated, and the decomposition formula suggests that the interval type-2 fuzzy entropy could be expressed as the weighted average of the fuzzy entropy, hesitant entropy and interval entropy. Finally, we construct two programming models based on the maximizing cross-entropy principle to determine attribute weights, and a novel MADM procedure is proposed and applied to a case study on the banks\u2019 liquidity risk evaluation.<\/jats:p>","DOI":"10.3233\/jifs-161188","type":"journal-article","created":{"date-parts":[[2017,8,4]],"date-time":"2017-08-04T11:36:54Z","timestamp":1501846614000},"page":"1809-1821","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Interval type-2 fuzzy information measures and their applications to attribute decision-making approach"],"prefix":"10.1177","volume":"33","author":[{"given":"Dengbao","family":"Yao","sequence":"first","affiliation":[{"name":"Economics School, Anhui University, Hefei, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cuicui","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Foundation, 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