Paper Info
Title
A discussion on fuzzy cardinality and quantification. Some applications in image processing.
Abstract
In this paper we discuss on some different representations of the cardinality of a fuzzy set and their use in fuzzy quantification. We have considered the widely employed sigma-count, fuzzy numbers, and gradual numbers. Gradual numbers assign numbers to values of a relevance scale, typically [0,1]. Contrary to sigma-count and fuzzy numbers, they provide a precise representation of the cardinality of a fuzzy set. We illustrate our claims by calculating the cardinality of the fuzzy set of pixels that match a certain fuzzy color in an image. For that purpose we consider fuzzy color spaces previously defined by the authors, consisting of a collection of fuzzy sets providing a suitable, conceptual quantization with soft boundaries of crisp color spaces. Finally, we show the suitability of our approaches to fuzzy quantification for different applications in image processing. First, the calculation of histograms. Second, the definition of the notion of dominant fuzzy color, and the calculation of the degree to which we can say that a certain color is dominant in an image.
Year
DOI
Venue
2014
10.1016/j.fss.2013.05.009
Fuzzy Sets and Systems
Keywords
Field
DocType
Representation by levels,Fuzzy cardinalities,Color histograms,Dominant color,Gradual numbers,Fuzzy color spaces
Discrete mathematics,Fuzzy classification,Defuzzification,Fuzzy set operations,Fuzzy logic,Fuzzy mathematics,Algorithm,Fuzzy set,Type-2 fuzzy sets and systems,Fuzzy number,Mathematics
Journal
Volume
Issue
ISSN
257
C
0165-0114
Citations 
PageRank 
References 
4
0.41
30
Authors
4
Name
Order
Citations
PageRank
Jesús Chamorro-Martínez16714.73
Daniel Sánchez212415.47
José M. Soto-Hidalgo3375.66
Pedro Manuel Martínez-Jiménez440.41