Fuzzy implication functions are one of the main operations in
fuzzy logic. They generalize the classical implication, which takes
values in the set {0,1}, to fuzzy logic, where the truth values
belong to the unit interval 0,1]. These functions are not only
fundamental for fuzzy logic systems, fuzzy control, approximate
reasoning and expert systems, but they also play a significant role
in mathematical fuzzy logic, in fuzzy mathematical morphology and
image processing, in defining fuzzy subsethood measures and in
solving fuzzy relational equations.
This volume collects 8 research papers on fuzzy implication
functions.
Three articles focus on the construction methods, on different
ways of generating new classes and on the common properties of
implications and their dependencies. Two articles discuss
implications defined on lattices, in particular implication
functions in interval-valued fuzzy set theories. One paper
summarizes the sufficient and necessary conditions of solutions for
one distributivity equation of implication. The following paper
analyzes compositions based on a binary operation * and discusses
the dependencies between the algebraic properties of this operation
and the induced sup-* composition. The last article discusses some
open problems related to fuzzy implications, which have either been
completely solved or those for which partial answers are known.
These papers aim to present today s state-of-the-art in this
area.
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