Beliakov, Gleb and James, Simon 2012, Defining Bonferroni means over lattices, in FUZZ-IEEE 2012 : Proceedings of the IEEE 2012 International Conference on Fuzzy Systems, IEEE Computer Society, Los Alamitos, Calif., pp. 67-74, doi: 10.1109/FUZZ-IEEE.2012.6250775.
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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Field of Research
080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective
970108 Expanding Knowledge in the Information and Computing Sciences
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