Abstract
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, overlap** 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 overlap** triangular, with equal width is limited when Computer-Aided Web Interviewing is applied. Respondents tend to use asymmetric fuzzy numbers with overlap** 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.
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Acknowledgements
The study was partly conducted in the framework of the research project entitled Households’ equipment with durable goods in statistical analysis and econometric modelling of material well-being. Project no. 2018/29/B/HS4/01420 is financed by the National Science Centre, Poland.
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Dziechciarz, J., Dziechciarz-Duda, M. (2021). Distance Measurement When Fuzzy Numbers Are Used. Survey of Selected Problems and Procedures. In: Chadjipadelis, T., Lausen, B., Markos, A., Lee, T.R., Montanari, A., Nugent, R. (eds) Data Analysis and Rationality in a Complex World. IFCS 2019. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-60104-1_5
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