A generalization of the Bonferroni mean based on partitions

Paper recently presented at FUZZIEEE in Hyderabad, India.  This was a joint work with Radko Mesiar and continues our work on generalizing the Bonferroni mean, facilitating the modeling of mandatory requirements.

Title: A generalization of the Bonferroni mean based on partitions

Authors: G. Beliakov, S. James and R. Mesiar

Abstract:

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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