A generalization of the Bonferroni mean based on partitions

0399787 - ÚTIA 2014 RIV US eng C - Conference Paper (international conference)
Beliakov, G. - James, S. - Mesiar, Radko
A generalization of the Bonferroni mean based on partitions.
Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ 2013). Piscataway: IEEE, 2013. ISBN 978-1-4799-0020-6. ISSN 1098-7584.
[2013 IEEE International Conference on Fuzzy Systems. Hyderabad (IN), 07.07.2013-10.07.2013]
R&D Projects: GA ČR GAP402/11/0378
Institutional support: RVO:67985556
Keywords : Aggregation functions * Bonferroni mean * Mandatory criteria * Decision making
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2013/E/mesiar-0399787.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0228632