Journal ArticleDOI
On the perimeter and area of fuzzy sets
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TLDR
The present note defines a projection operator that should be used along with the multiplicative conjunction in the process of fuzzy reasoning and shows that the perimeter, diameter, and height fit more comfortably with the notion of area.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1987-08-01. It has received 39 citations till now. The article focuses on the topics: Fuzzy set & Fuzzy number.read more
Citations
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Fuzzy distance transform: theory, algorithms, and applications
TL;DR: The theoretical framework of FDT in continuous space is extended to digital cubic spaces and it is shown that for any fuzzy digital object, fuzzy distance is a metric for the support of the object.
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Fuzzy plane geometry I: points and lines
TL;DR: A comprehensive study of fuzzy geometry is introduced by first defining a fuzzy point and a fuzzy line in fuzzy plane geometry and showing it is a (weak) fuzzy metric.
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Fuzzy plane geometry II: circles and polygons
TL;DR: It is shown that the fuzzy area of a fuzzy circle, or a fuzzy polygon, is a fuzzy number and it is argued that the fuzziest perimeter of a fuzzier circle or polygon is a fuzziest number.
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Measurements of digitized objects with fuzzy borders in 2D and 3D
TL;DR: The method suggested provides significant improvement in precision, compared to analogous estimation results obtained on a crisp (hard) segmentation, especially in the case of low resolution images.
References
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Journal ArticleDOI
Su una teoria generale della misura (r − 1)-dimensionale in uno spazio adr dimensioni
TL;DR: In this article, a definizione della misura (r − 1)-dimensionale della frontiera orientata di un insieme diBorel contenuto in uno spazio euclideo ad r dimensioni and dimostro alcune fra le piu notevoli proprieta di tale misura.
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Additive fuzzy measures and integrals, III
TL;DR: A new concept of “disjointness” for fuzzy is introduced and studied, and a concept of an “additive class of fuzzy sets” is defined to be a class of fuzzy sets closed under some ‘additive operations’.
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The perimeter of a fuzzy set
Azriel Rosenfeld,Seymour Haber +1 more
TL;DR: This paper proposes a definition of perimeter for fuzzy subsets of the plane and shows that it reduces to the standard definition if the fuzzy subset is an ordinary subset.