Abstract: Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF-)F-soft lattice implication algebras) are introduced. Basic properties of (IF-)F-soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(2, 2 _qk)((2, 2 _ qk))-fuzzy (implicative) filter) of L are introduced, which are generalizations of fuzzy (implicative) filters. Some characterizations for a soft set to be a (IF-)F-soft lattice implication algebra are provided. Analogously, this idea can be used in other types of filteristic lattice implication algebras (such as fantastic (positive implicative) filteristic soft lattice implication algebras).
Abstract: Noise contamination in a magnetic resonance (MR)
image could occur during acquisition, storage, and transmission in
which effective filtering is required to avoid repeating the MR
procedure. In this paper, an iterative asymmetrical triangle fuzzy
filter with moving average center (ATMAVi filter) is used to reduce
different levels of salt and pepper noise in a brain MR image. Besides
visual inspection on filtered images, the mean squared error (MSE) is
used as an objective measurement. When compared with the median
filter, simulation results indicate that the ATMAVi filter is effective
especially for filtering a higher level noise (such as noise density =
0.45) using a smaller window size (such as 3x3) when operated
iteratively or using a larger window size (such as 5x5) when operated
non-iteratively.