Abstract
We like to present a study of the fuzzy approach to intelligent counting. The result of counting in a fuzzy set is then itself a fuzzy set of nonnegative integers. We will define and investigate various types of fuzzy cardinalities. In each case, similarly to the scalar approach from Chapter 8, we will emphasize that they reflect and formalize the results of real counting methods used by human beings when counting under information imprecision. An especially interesting type of fuzzy cardinalities are so-called FECounts. Their connections with classification and similarity measures as well as a look at FECounts through rule-based systems and the Bellman-Zadeh model of decision making will be presented.
Finally, we like to deal with counting under imprecision combined with incompleteness of information about the objects of counting. To that end, fuzzy cardinalities will be extended to interval-valued fuzzy sets and I-fuzzy sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wygralak, M. (2013). Fuzzy Approach. In: Intelligent Counting Under Information Imprecision. Studies in Fuzziness and Soft Computing, vol 292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34685-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-34685-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34684-2
Online ISBN: 978-3-642-34685-9
eBook Packages: EngineeringEngineering (R0)