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.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Field of Research
080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective
970108 Expanding Knowledge in the Information and Computing Sciences
Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved.
Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO.
If you believe that your rights have been infringed by this repository, please contact email@example.com.
Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact firstname.lastname@example.org.