A generalization of the Bonferroni mean based on partitions
Beliakov, Gleb, James, Simon and Radko, Mesiar 2013, A generalization of the Bonferroni mean based on partitions, in FUZZ-IEEE 2013 : Proceedings of the IEEE International Conference on Fuzzy Systems, IEEE Computational Intelligence Society, Piscataway, N.J., doi: 10.1109/FUZZ-IEEE.2013.6622348.
The mean defined by Bonferroni in 1950 (known by the same name) averages all non-identical product pairs of the inputs. Its generalizations to date have been able to capture unique behavior that may be desired in some decision-making contexts such as the ability to model mandatory requirements. In this paper, we propose a composition that averages conjunctions between the respective means of a designated subset-size partition. We investigate the behavior of such a function and note the relationship within a given family as the subset size is changed. We found that the proposed function is able to more intuitively handle multiple mandatory requirements or mandatory input sets.
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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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