Measurement of Membership Functions: Theoretical and Empirical Work

The Role of Vague Categories in Semantic and Adaptive Web Interfaces

“…Membership functions of vague categories are a way to express fuzzy degrees of belonging that can be used instead. These membership functions can be obtained from experts as approximations, or they can be obtained directly from users, by mean of existing membership elicitation techniques [5]. In the context of Web applications, a number of factors influencing the overall usability of the page have been studied [14], including amount of text, number and type of links and images, color use and page length.…”

“…In some cases, this enables being consistent with existing elicitation studies that question the validity of some "classical" hedges. For example, the V ERY hedge is usually represented simply as µ V ERY −A (x) = µ A (x) 2 , while several experimental studies (summarized in [5]) report a shift in the membership function.…”

Elicitation of membership functions: how far can theory take us?

“…The measurement view is in the connection of subjective and objective views in the sense that the problem can be defined in both ways depending on the observer(s) who is (are) making the comparison. The comparisons can be results of subjective evaluations or results of "precise" (or idealized) measurements (see [5] for more details on each interpretation).…”

“…One can identify eight major methods of eliciting membership functions (see [5] for details and original references):…”

“…Figure 4 shows which type of elicitation method is appropriate for each interpretation of fuzzy membership function based on results from measurement theory [2,3,4]. There is a large body of empirical research (mostly in the psychology literature) about elicitation methods of fuzzy membership functions (see [5] for a review). The elicitation methods shown in Figure 4 has been compiled from that body of work.…”