Characterization of some functions stable for positive linear transformations

[en] This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered weighted averaging operators (OWA) introduced by Yager in 1988.

Disciplines :

Mathematics

Author, co-author :

Marichal, Jean-Luc

Mathonet, Pierre ; Université de Liège - ULiège > Département de mathématique > Département de mathématique

Tousset, E.

Language :

English

Title :

Characterization of some functions stable for positive linear transformations

Publication date :

1999

Journal title :

Fuzzy Sets and Systems

ISSN :

0165-0114

eISSN :

1872-6801

Publisher :

Elsevier Science, Amsterdam, Netherlands

Volume :

102

Pages :

293-314

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 09 July 2010

Statistics

Number of views

31 (2 by ULiège)

Number of downloads

104 (3 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392-400.
J. Aczél, Lectures on Functional Equations and Applications, Academic Press, New York, 1966.
J. Aczél, On weighted synthesis of judgements, Aequationes Math. 27 (1984) 288-307.
J. Aczél, C. Alsina, Synthesizing judgments: A functional equations approach, Math. Modelling 9 (1987) 311-320.
J. Aczél, F.S. Roberts, On the possible merging functions, Math. Social Sci. 17 (1989) 205-243.
J. Aczél, F.S. Roberts, Z. Rosenbaum, On scientific laws without dimensional constants, J. Math. Anal. Appl. 119 (1986) 389-416.
J. Fodor, J.-L. Marichal, On nonstrict means, Aequationes Math., in press.
J. Fodor, J.-L. Marichal, M. Roubens, Characterization of some aggregation functions arising from MCDM problems, in: Proc. IPMU'94, Paris, pp. 1026-1031.
J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.
A.N. Kolmogoroff, Sur la notion de la moyenne, Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12 (1930) 388-391.
C.H. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 189-212.
J.-L. Marichal, P. Mathonet, A characterization of the ordered weighted averaging functions based on the ordered bisymmetry property, IEEE Trans. Fuzzy Systems, submitted.
J.-L. Marichal, M. Roubens, Characterization of some stable aggregation functions, in: Proc. Internat. Conf. on Industrial Engineering and Production Management, Mons, Belgique, pp. 187-196.
M. Nagumo, Über eine Klasse der Mittelwerte, Japan. J. Math. 6 (1930) 71-79.
F.S. Roberts, Measurement Theory with Applications to Decision-making, Utility and the Social Sciences, Addison-Wesley, Reading, MA.
W. Silvert, Symmetric summation: A class of operations on fuzzy sets, IEEE Trans. Systems Man Cybernet. 9 (1979) 657-659.