On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Beliakov, Gleb and James, Simon 2013, On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts, Fuzzy sets and systems, vol. 211, pp. 84-98.

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Title On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts
Author(s) Beliakov, Gleb
James, Simon
Journal name Fuzzy sets and systems
Volume number 211
Start page 84
End page 98
Total pages 15
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2013-01-16
ISSN 0165-0114
1872-6801
Keyword(s) aggregation operators
atanassov intuitionistic fuzzy sets
interval valued fuzzy sets
means
Summary Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.
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 C1 Refereed article in a scholarly journal
Copyright notice ©2012, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30044976

Document type: Journal Article
Collection: School of Information Technology
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