Defining Bonferroni means over lattices

New paper accepted to FUZZ IEEE

Title: Defining Bonferroni means over lattices

Authors: Beliakov, G. and James, S.


In the face of mass amounts of information and the need for transparent and
fair decision processes, aggregation functions are essential for summarizing
data and providing overall evaluations. Although families such as weighted
means and medians have been well studied, there are still applications for
which no existing aggregation functions can capture the decision makers’
preferences. Furthermore, extensions of aggregation functions to lattices are
often needed to model operations on L-fuzzy sets, interval-valued and
intuitionistic fuzzy sets.
In such cases, the aggregation properties need to be considered in
light of the lattice
structure, as otherwise counterintuitive or unreliable behavior may result.

The Bonferroni mean has recently received attention in the fuzzy sets and
decision making community as it is able to model useful notions such as
mandatory requirements. Here, we consider its associated penalty function
to extend the generalized Bonferroni mean to lattices. We show that
different notions of dissimilarity on lattices can lead to
alternative expressions.



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