In all studies of user's behavior on searching the Web, researchers found that their search strategy or traversal process showed a pattern of moving back and forth between searching and browsing. These activities of searching and browsing are inclusive activities to complete a goal-oriented task to find the answer for the query. The moving back and forth, including backtracking to a former Web page, constitutes the measurable or physical states or actions that a user takes while searching the Web. How do we account for the repeated searching and browsing and shifting between different Web pages to better understand the behavior of users? Is there a mathematical model that can help model actions of users to distinguish between two users while their repeated actions are accounted for since it is a part of their behavior or inherent essence to arrive at the goal of answering the questions regardless whether they are successful or unsuccessful? The idea of a set does not help account for repeated actions since in a set repeated objects are ignored. In some situations, we want a structure in which a collections of objects in the same sense as a set but a redundancy counts. The structure of a bag as a framework can help study the behavior Of users and uncover some intrinsic properties about users. Also would bags help distinguish between two sets of users based on their syntactic properties without a priori knowledge of their semantic properties'? This study constitutes a premier in applying bags to user's mining of the Web. The research will consider queries that depend on one variable or "univariable." An example of "univariable" queries is "Find the number of Web pages of users whose searching is less than the average." Crisp bags failed to answer such a query. Fuzzy operators were used successfully in comparing the "fuzzy bag" of the successful users to the "fuzzy bag" of unsuccessful users to answer such a query. A distance between two fuzzy bags was also established. The research also considered queries that depend on more than one variable or multivariable. An example of a "multivariable" query is "Find the number of Web pages of users whose number of searches is less than average and hyperlink navigation is less than the average." One-dimensional fuzzy bags were extended to two-dimensional fuzzy bags and two-dimensional fuzzy bag operators were used to answer such a query. (C) 2009 Wiley Periodicals, Inc.
