Distance Measurement When Fuzzy Numbers Are Used. Survey of Selected Problems and Procedures

The goal is to identify and to discuss distance and dissimilarity measures calculated with fuzzy numbers. It is crucial to define the distance and dissimilarity measures for unconventional fuzzy numbers, i.e. asymmetric, overlapping triangular, with unequal width. Resulting distance measures are to be used for clustering and linear ordering of objects. The method applied consists of an attempt to identify and to discuss the applicability of specialised techniques for unconventional fuzzy measurement. The emphasis is put on distance (similarity and dissimilarity) of measurement concepts when unconventional fuzzy numbers are used. The use of conventional fuzzy numbers, i.e. symmetric, not overlapping triangular, with equal width is limited when Computer-Aided Web Interviewing is applied. Respondents tend to use asymmetric fuzzy numbers with overlapping shape and unequal width. Several problems arise in the multivariate statistical analysis of measurement results. Proposals from pattern recognition literature are not applicable and new methods based on directed fuzzy numbers are involved.