Midpoints for fuzzy sets and their application in medicine.
Artificial Intelligence in Medicine (Impact Factor: 1.36).
02/2003; 27(1):81-101. DOI: 10.1016/S0933-3657(02)00080-5
Source: PubMed  ABSTRACT Using Kosko's hypercube, we identify a
fuzzy set with a point in a unit hypercube. A non-fuzzy or crisp
subset of a set is a vertex of the hypercube. We introduce some
new ideas: the definition of the fuzzy segment joining two given
fuzzy subsets of a set, the set of midpoints between those two
fuzzy subsets, and the set of equidistant points from given
points. We present some basic properties and relations between
these concepts and provide a complete description of fuzzy
segments and midpoints. In the majority of cases, there is no
unique midpoint; one has an infinite set of possibilities to
choose from. This situation is totally different from classical
Euclidean geometry where, for two given points, there is a
unique midpoint. We use the obtained results to study two sets
of medical data and present two ap