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.
