The durations of events in real world are difficult to measure precisely. The starting points and ending points of events are fuzzy. It makes it difficult to describe the fuzzy time intervals of events in Allen's interval algebra. The concept of duration density function of events to represent the durations of events is used. Time intervals to represent time duration density function is used approximately. Allen's interval algebra to have the temporal reasoning can be used.
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胡广朋 凌青华 于枫. 端点模糊的区间代数[J]. 科学技术与工程, 2006, (22): 3564-3566. HU Guangpeng, LING Qinghua, YU Feng. The Interval Algebra with Fuzzy Endpoints[J]. Science Technology and Engineering,2006,(22):3564-3566.