Interval-valued fuzzy sets constructed from matrices: Application to edge detection

In this paper we present a method to construct interval-valued fuzzy sets (or interval type 2 fuzzy sets) from a matrix (or image), in such a way that we obtain the length of the interval representing the membership of any element to the new set from the differences between the values assigned to th...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 160; no. 13; pp. 1819 - 1840
Main Authors Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.07.2009
Elsevier
Subjects
Applied sciences
Circuit properties
Computer science; control theory; systems
Control theory. Systems
Digital circuits
Edge detector
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Information, signal and communications theory
Interval-valued fuzzy entropy
Interval-valued fuzzy set
Mathematical methods
Miscellaneous
s-Representable interval-valued fuzzy t-conorm
System theory
t-Representable interval-valued fuzzy t-norm
Telecommunications and information theory
Theoretical computing
Interval-valued fuzzy set
t-Representable interval-valued fuzzy t-norm
s-Representable interval-valued fuzzy t-conorm
Edge detector
Interval-valued fuzzy entropy
Engineering
Fuzzy system
Information processing
Entropy
Fuzzy set
Edge detection
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Summary:In this paper we present a method to construct interval-valued fuzzy sets (or interval type 2 fuzzy sets) from a matrix (or image), in such a way that we obtain the length of the interval representing the membership of any element to the new set from the differences between the values assigned to that element and its neighbors in the starting matrix. Using the concepts of interval-valued fuzzy t-norm, interval-valued fuzzy t-conorm and interval-valued fuzzy entropy, we are able to detect big enough jumps (edges) between the values of an element and its neighbors in the starting matrix. We also prove that the unique t-representable interval-valued fuzzy t-norms and the unique s-representable interval-valued fuzzy t-conorms that preserve the length zero of the intervals are the ones generated by means of the t-norm minimum and the t-conorm maximum.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2008.08.005