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Fuzzy regions: interpretations of surface area and distance

Verstraete J.

Control and Cybernetics

2009

Vol. 38, no 2

509-526

This contribution concerns the modelling of fuzzy information in geographic databases. For this purpose, fuzzy regions and fuzzy points have been defined in the past, along with a number of suitable operations. For numerical information - such as the surface area of fuzzy regions, or the distance between fuzzy regions and/or fuzzy points - the computation depends on the interpretation given to the fuzzy regions or points. Consequently, it is important to differentiate between the interpretation in order to obtain correct results. This article explains in detail the impact of the interpretation in terms of both the surface area and the distance.

The transportation distance for fuzzy descriptions of measurements

Allevard T., Benoit E., Foulloy L.

Metrology and Measurement Systems

2007

Vol. 14, nr 1

25-37

Fuzzy nominal scales were introduced in order to propose a formalism to the representation of empirical quantities by fuzzy subsets of words. This scale proposes a similarity relation and an associated bounded distance that can be used to perform signal processing on fuzzy subsets of words. Due to the limits of this last distance, we studied distances associated to this formalism and proposed a new distance operator named transportation distance. This paper presents the results of these studies.