Defining Bonferroni means over lattices

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.

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Title Defining Bonferroni means over lattices
Author(s) Beliakov, Gleb
James, Simon
Conference name International Conference on Fuzzy Systems (2012 : Brisbane, Qld.)
Conference location Brisbane, Qld.
Conference dates 10-15 Jun. 2012
Title of proceedings FUZZ-IEEE 2012 : Proceedings of the IEEE 2012 International Conference on Fuzzy Systems
Editor(s) [Unknown]
Publication date 2012
Conference series International Conference on Fuzzy Systems
Start page 67
End page 74
Total pages 8
Publisher IEEE Computer Society
Place of publication Los Alamitos, Calif.
Keyword(s) aggregates
Australia
context
fuzzy logic
fuzzy sets
lattices
vectors
Summary 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.
ISBN 9781467315050
ISSN 1098-7584
Language eng
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category E1 Full written paper - refereed
Copyright notice ©2012, IEEE
Persistent URL http://hdl.handle.net/10536/DRO/DU:30049229

Document type: Conference Paper
Collection: School of Information Technology
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