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Top1. Introduction
The prompt development and wide applications of the Web technologies have resulted in the availability of huge amounts of Web data. The data representation and exchange on the Web are increasingly important. Being a standard recommended by W3C (World Wide Web Consortium), XML (eXtensible Markup Language) has been the de-facto standard of data representation and exchange on the Web (XML, 2015), which allows the easy development of applications that exchange data over the Web. In the context of deep Web, data in relational databases are extracted to XML documents, which are then published on the Web. Mapping relational databases into XML is essential for XML data management (Fong & Shiu, (2012;Fong, Wong & Cheng, 2003; Lee, Mani, Chiu & Chu, 2001; Liu, Vincent & Liu, 2006).
Data in the real-world applications are diverse and some data are inherently uncertain. Human knowledge and natural language, for example, have a big deal of uncertainty. To deal with uncertain data, two major foundations have been developed (Parsons, 1996), which are probability theory for objective uncertainty and fuzzy sets for subjective uncertainty, respectively. Also, Dempster-Shafer theory (also known as belief theory or evidence theory (Yager & Alajlan, 2015)) is applied. Subjective uncertainty comes from subjective estimation and judgment made by human, for example, “young” for age and “hot” for temperature. Objective uncertainty comes from objective statistics instead of subjective estimation and judgment, for example, possible orientation of landing on for a coin being tossed.
Fuzzy sets and probability theory have widely been applied to extend various database models (Meged & Gelbard, 2012), including the uncertain relational database model (e.g., the fuzzy one (Buckles & Petry, 1982; Ma, 2005; Prade & Testemale, 1984; Tayal & Saxena, 2015; Yang, Zhang, Liu, Wu, Yu, Nakajima & Rishe, 2001) and the probabilistic one (Barbara, Garcia-Molina & Porter, 1992; Dalvi, Re & Suciu, 2011; Dey & Sarkar, 1996; Lakshmanan, Leone, Ross & Subrahmanian, 1997; Pittarelli, 1994; Murthy, Ikeda & Widom, 2011; Zhu, Zhang, Cao & Tang, 2016) and the uncertain object-oriented database model (e.g., the fuzzy one (Delgado, Marín, Pérez & Vila, 2016; Ma, Zhang & Ma, 2004; Yan & Ma, 2014a) and the probabilistic one (Eiter, Lu, Lukasiewicz & Subrahmanian, 2001; Kornatzky & Shimony, 1994; Nuray-Turan, Kalashnikov, Mehrotra & Yu, 2012)). In the context of XML, some recent efforts have devoted on the uncertain XML (e.g., the probabilistic one (Kimelfeld & Senellart, 2013) and the fuzzy one (Ma & Yan, 2007; Ma, Liu & Yan, 2010)) to handle uncertain data on the Web. More important, several efforts have been carried out to map uncertain relational databases (Amarilli & Senellart, 2013; Ma & Yan, 2007) from or to uncertain XML model. Being similar with the classical XML data management (Fong & Shiu, 2012), mapping uncertain relational databases to XML serves as uncertain data representation and exchange on the Web.