PROCEEDINGS IPMU '08

Central points and approximation in residuated lattices

Radim Belohlavek, Michal Krupka.

Given a subset B of a complete
residuated lattice, what are its
points which are reasonably close
to any point of B? What are the
best such points? In this paper, we
seek to answer these questions provided
closeness is assessed by means
of biresiduum, i.e. the truth function
of equivalence in fuzzy logic. In
addition, we present two algorithms
which output, for a given input set
M of points in a residuated lattice,
another set K which approximates
M to a desired degree. We prove
that the algorithms are optimal in
that the set K is minimal in terms
of the number of its elements. Moreover,
we show that the elements of
any set K' with such property are
bounded from below and from above
by the elements produced by the two
algorithms.

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