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Articles

Invariant continuous aggregation functions

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Pages 177-188 | Received 25 Nov 2008, Accepted 04 Nov 2009, Published online: 29 Dec 2009

References

  • Aczél , J. 1966 . “ Lectures on functional equations and their applications ” . In Mathematics in science and engineering , Vol. 19 , New York : Academic Press .
  • Aczél , J. , Roberts , F.S. and Rosenbaum , Z. 1986 . On scientific laws without dimensional constants . Journal of mathematical analysis and application , 119 ( 1–2 ) : 389 – 416 .
  • Aczél , J. and Roberts , F.S. 1989 . On the possible merging functions . Mathematical social sciences , 17 ( 3 ) : 205 – 243 .
  • Adem , J. and Gochet , W. 2008 . Counting and enumerating aggregate classifiers . Discrete applied mathematics , 156 : 2459 – 2468 .
  • Bioch , J.C. and Ibaraki , T. 1995 . Decompositions of positive self-dual Boolean functions . Discrete mathematics , 140 : 23 – 46 .
  • Bioch , J. and Ibaraki , T. 1995 . Generating and approximating nondominated coteries . IEEE transactions on parallel and distributed systems , 6 ( 9 ) : 905 – 914 .
  • Choquet , G. 1953–1954 . Theory of capacities . Annales de l'institut Fourier , 5 : 31 – 295 .
  • Couceiro , M. , Foldes , S. and Lehtonen , E. 2006 . Composition of post classes and normal forms of Boolean functions . Discrete mathematics , 306 ( 24 ) : 3223 – 3243 .
  • Denneberg , D. 1994 . Non-additive measure and integral , Dordrecht : Kluwer .
  • Grabisch , M. 2009 . Aggregation functions , Cambridge : Cambridge University Press . (in press)
  • Hammer , P.L. and Rudeanu , S. 1968 . Boolean methods in operational research and related areas , Berlin : Springer .
  • Hillier , F.S. and Lieberman , G.J. 2005 . Introduction to operations research , Boston, MA : McGraw-Hill .
  • Jablonski , S.W. , Jablonski , S.W. , Gawrilow , G.P. and Kudrjawzew , W.B. 1970 . Boolesche Funktionen und Postsche Klassen , Braunschweig : Vieweg .
  • Klir , G.J. and Folger , T.A. 1998 . Fuzzy sets, uncertainty and information , New Jersey, NJ : Prentice Hall .
  • Kolesárová , A. and Komorníková , M. 1999 . Triangular norm-based iterative compensatory operators . Fuzzy sets and systems , 104 ( 1 ) : 109 – 120 .
  • Lau, D., 2006. Function algebras on finite sets – a basic course on many-valued logic and clone theory. Springer Monographs in Mathematics, 2006
  • Marichal , J.-L. 2002 . “ Aggregation of interacting criteria by means of the discrete Choquet integral ” . In Aggregation operators: new trends and applications , Edited by: Calvo , T. 224 – 244 . Heidelberg : Physica .
  • Mesiar , R. and Rückschlossová , T. 2004 . Characterization of invariant aggregation operators . Fuzzy sets and systems , 142 ( 1 ) : 63 – 73 .
  • Muroga , S. , Tsuboi , T. and Baugh , C R. 1970 . Enumeration of threshold functions of eight variables . IEEE transactions on computers , C-19 ( 9 ) : 818 – 825 .
  • Muroga , S. 1971 . Threshold logic and its applications , New York : Wiley .
  • Ovchinnikov , S. and Dukchovny , A. 2000 . Integral representation of invariant functionals . Journal of mathematical analysis and application , 244 ( 1 ) : 228 – 232 .
  • Pap , E. 1995 . “ Null-additive set functions ” . In Volume 337 of mathematics and its applications , Dordrecht : Kluwer .
  • Post , E.L. 1941 . The two-valued iterative systems of mathematical logic . Annals of mathematical studies , 5 : 1 – 122 .
  • Wang , Z. and Klir , G.J. 1992 . Fuzzy measure theory , New York, NY : Plenum Press .
  • Wang , Z. and Klir , G.J. 2009 . “ Generalized measure theory ” . In IFSR international series on systems science and engineering , Vol. 25 , New York, NY : Springer .

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