Characterization of some aggregation functions stable for positive linear transformations

Fuzzy Sets and Systems

Volumn 102, Issue 2, 1999, Pages 293-314

  Marichal, Jean Luc ^a   Mathonet, Pierre ^a   Tousset, Eric ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Aggregation functions; Algebraic properties of aggregation functions; Fuzzy multiple criteria decision making; Interval scale; Invariance

Indexed keywords

EID: 0003261005     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(97)00128-0     Document Type: Article

References (16)

1. J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392-400.
2. J. Aczél, Lectures on Functional Equations and Applications, Academic Press, New York, 1966.
3. J. Aczél, On weighted synthesis of judgements, Aequationes Math. 27 (1984) 288-307.
4. J. Aczél, C. Alsina, Synthesizing judgments: A functional equations approach, Math. Modelling 9 (1987) 311-320.
5. J. Aczél, F.S. Roberts, On the possible merging functions, Math. Social Sci. 17 (1989) 205-243.
6. J. Aczél, F.S. Roberts, Z. Rosenbaum, On scientific laws without dimensional constants, J. Math. Anal. Appl. 119 (1986) 389-416.
7. J. Fodor, J.-L. Marichal, On nonstrict means, Aequationes Math., in press.
8. J. Fodor, J.-L. Marichal, M. Roubens, Characterization of some aggregation functions arising from MCDM problems, in: Proc. IPMU'94, Paris, pp. 1026-1031.
9. J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.
10. A.N. Kolmogoroff, Sur la notion de la moyenne, Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12 (1930) 388-391.
11. C.H. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 189-212.
12. J.-L. Marichal, P. Mathonet, A characterization of the ordered weighted averaging functions based on the ordered bisymmetry property, IEEE Trans. Fuzzy Systems, submitted.
13. 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.
14. M. Nagumo, Über eine Klasse der Mittelwerte, Japan. J. Math. 6 (1930) 71-79.
15. F.S. Roberts, Measurement Theory with Applications to Decision-making, Utility and the Social Sciences, Addison-Wesley, Reading, MA.
16. W. Silvert, Symmetric summation: A class of operations on fuzzy sets, IEEE Trans. Systems Man Cybernet. 9 (1979) 657-659.