Measurement of membership functions: Theoretical and empirical work. (English) Zbl 0974.03046

Bilgiç, Taner; Türkşen, I. Burhan

Dubois, Didier (ed.) et al., Fundamentals of fuzzy sets. Foreword by Lotfi A. Zadeh. Dordrecht: Kluwer Academic Publishers. Handb. Fuzzy Sets Ser. 7, 195-230 (2000).

This paper presents a review of various interpretations of the fuzzy membership function, e.g. the likelihood view, the random set view, the similarity view, the utility view and the measurement view. In a second part ways of obtaining a membership function are presented, e.g. polling, direct rating, reverse rating, interval estimation, membership exemplification and pairwise comparison. The authors emphasize that different interpretations call for different elicitation methods and try to make this distinction clear using techniques from measurement theory.
For the entire collection see [Zbl 0942.00007].

Reviewer: Wolfgang Näther (Freiberg)

MSC:

03E72	Theory of fuzzy sets, etc.
03-02	Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations

Keywords:

fuzzy membership function; elicitation methods; measurement theory