Special fuzzy measures on infinite countable sets and related aggregation functions

While both additive and symmetric fuzzy measures on a finite universe are completely described by a probability distribution vector, this is no more the case of a countably infinite universe. After a brief discussion of additive fuzzy measures on positive integers, we characterize all symmetric fuzz...

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Bibliographic Details
Published in:Fuzzy sets and systems Vol. 167; no. 1; pp. 57 - 64
Main Author: STUPNANOVA, Andrea
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier B.V 30.03.2011
Elsevier
Subjects:
Additive fuzzy measure
Applied sciences
Choquet integral
Circuit properties
Computer science; control theory; systems
Digital circuits
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Fuzzy
Fuzzy logic
Fuzzy set theory
Information, signal and communications theory
Integers
k-Order additivity
Mathematical analysis
Mathematical methods
Mathematics
Measure and integration
Miscellaneous
Operators
OWA operator
p-Symmetry
Sciences and techniques of general use
Symmetric fuzzy measure
Telecommunications and information theory
Theoretical computing
Universe
Vectors (mathematics)
Symmetric fuzzy measure
k-Order additivity
OWA operator
Choquet integral
p-Symmetry
Additive fuzzy measure
Integer
Fuzzy system
Information processing
Probability distribution
Fuzzy set
ISSN:0165-0114, 1872-6801
Online Access:Get full text
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Description
Summary:While both additive and symmetric fuzzy measures on a finite universe are completely described by a probability distribution vector, this is no more the case of a countably infinite universe. After a brief discussion of additive fuzzy measures on positive integers, we characterize all symmetric fuzzy measures on integers by means of three constants and of two probability distribution vectors. OWA operators for n arguments were introduced by Yager in 1988. Grabisch in 1995 has shown representation of OWA operators by means of Choquet integral with respect to symmetric normed capacities. Based on symmetric capacities on positive integers, we extend the concept of OWA operators to infinitary sequences and thus we develop the concept of infinitary OWA operators.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2010.09.009