Complutense University Library

A discussion on aggregation operators.

Gomez, D. and Montero de Juan, Francisco Javier (2004) A discussion on aggregation operators. Kybernetika, 40 (1). pp. 107-120. ISSN 0023-5954

[img] PDF
Restricted to Repository staff only until 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


It has been lately made very clear that aggregation processes can not be based upon a unique binary operator. Global aggregation operators have been therefore introduced as families of aggregation operators {Tn}n , being each one of these Tn the n-ary operator actually amalgamating information whenever the number of items to be aggregated is
n. Of course, some mathematical restrictions can be introduced, in order to assure an appropriate meaning, consistency and key mathematical capabilities. In this paper we shall discuss these standard conditions, pointing out their respective relevance.

Item Type:Article
Uncontrolled Keywords:Aggregation rules; Logical connectives; Fuzzy sets
Subjects:Sciences > Computer science > Artificial intelligence
Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:16683

J. Aczel: Lectures on Functional Equations and Their Applications. Academic Press, New York 1966.

A. Amo, J. Montero, G. Biging, and V. Cutello: Fuzzy classification systems. European J. Oper. Res. (to appear).

A. Del Amo, J. Montero, and E. Molina: Additive recursive rules. In: Preferences and Decisions Under Incomplete Knowledge (J. Fodor et al, eds.), Physica-Verlag,Heidelberg 2000.

A. Del Amo, J. Montero, and E. Molina: Representation of consistent recursive rules. European J. Oper. Res. 30 (2001), 29-53.

A. del Amo, J. Montero, and G. Biging: Classifying pixels by means of fuzzy relations. Internat. J. Gen. Systems 29 (2000), 605-621.

A. Amo, J. Montero, A. Fernandez, M. Lopez, J. Tordesillas, and G. Biging: Spectral fuzzy classification: an application. IEEE Trans. Systems, Man and Cybernetics 32 (2002), 42 48.

R. E. Barlow and F. Proschan: Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring 1981.

K. Y. Cai: Introduction to Fuzzy Reliability. Kluwer,Boston 1996.

T. Calvo, G. Mayor, and R. Mesiar (eds.): Aggregation Operators. Physica Verlag, Heidelberg 2002.

T. Calvo, A. Kolesarova, M. Komornikova, and R. Mesiar: Aggregation operators:properties, classes and construction methods. In: Aggregation Operators (T. Calvo et al, eds.), Physica-Verlag, Heidelberg 2002, pp. 3-104.

V. Cutello and J. Montero: Recursive families of OWA operators. In: Proc. FUZZIEEE Conference (P.P. Bonisone, ed.), IEEE Press, Piscataway 1994, pp. 1137-1141.

V. Cutello and J. Montero: Hierarchical aggregation of OWA operators: basic measures and related computational problems. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 3 (1995), 17-26.

V. Cutello and J. Montero: Recursive connective rules. Intelligent Systems 14 (1999), 3-20.

B. De Baets: Idempotent uninorms. European J. Oper. Res. 118 (1999), 631-642.

J. Dombi: Basic concepts for a theory of evaluation: the aggregative operator. European J. Oper. Res. 10 (1982), 282-293.

J. C. Fodor and M. Roubens: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht 1994.

L.W. Fung and K. S. Fu: An axiomatic approach to rational decision making in a fuzzy environment. In: Fuzzy Sets and Their Applications to Cognitive and Decision Processes (L. Zadeh et al, eds.), Academic Press, New York 1975, pp. 227-256.

M. C. Golumbic: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York 1980.

D. Gomez, J. Montero, J. Yafiez, J. Gonzalez-Pachon, and V. Cutello: Crisp dimension theory and valued preference relations. Internat. J. Gen. Systems (to appear).

E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms. Kluwer, Dordrecht 2000.

E. P. Klement, R. Mesiar, and E. Pap: On the relationship of associative compensatory operators to triangular norms and conorms. Internat. J. Uncertainty, Fuzziness and

Knowledge-based Systems 4 (1996), 129-144.

G.J. Klir and T. A. Folger: Fuzzy Sets, Uncertainty and Information. Prentice Hall, London 1988.

A. Kolesarova and M. Komornikova: Triangular norm-based iterative compensatory operators. Fuzzy Sets and Systems 104 (1999), 109-120.

K. T. Mak: Coherent continuous systems and the generalized functional equation of associativity. Mathem. Oper. Res. 12 (1987),597-625.

J. L. Marichal, P. Mathonet, and E. Tousset: Characterization of some aggregation functions stable for positive linear transformations. Fuzzy Sets and Systems 102 (1999),293-314.

M. Mas, G. Mayor, J. Surier, and J. Torrens: Generation of multi-dimensional aggregation functions. Mathware and Soft Computing 5 (1998), 233-242.

M. Mas, G. Mayor, and J. Torrens: T-operators. Internat. J. Uncertainty, Fuzziness and Knowledge-based Systems 7(1999), 31-50.

G. Mayor and T. Calvo: On extended aggregation functions. In: Proc. IFSA Conference,Volume 1, Academia, Prague 1997, pp. 281-285.

K. Menger: Statistical methods. Proc. Nat. Acad. Sci. U.S.A. 8 (1942), 535-537.

R. Mesiar: Compensatory operators based on triangular norms and conorms. In: Proc.EUFIT Conference (H.-J. Zimmermann, ed.), Elite Foundation, Aachen 1995, pp. 131 135.

R. Mesiar and M. Komornikova: Aggregation operators. In: Proc. PRIM Conference,Institute of Mathematics, Novi Sad 1997, pp. 193 211.

R. Mesiar and M. Komornikova: Triangular norm-based aggregation of evidence under fuzziness. In: Aggregation and Fussion of Imperfect Information (B. Bouchon Meunier, ed.), Physica-Verlag, Heidelberg 1998, pp. 11-35.

J. Montero: A note on Fung Fu's theorem. Fuzzy Sets and Systems 17(1985), 259 269.

J. Montero: Aggregation of fuzzy opinions in a fuzzy group. Fuzzy Sets and Systems 25 (1988), 15 20.

J. Montero, A. Amo, E. Molina, and V. Cutello: On the relevance of OWA rules. In:Proc. IPMU Conference, Volume 2, Universidad Politecnica de Madrid, Madrid 2000,pp. 992 996.

J. Montero, J. Tejada, and J. Yariez: Structural properties of continuous systems. European J. Oper. Res. 45 (1990), 231-240.

P. Pattanaik: Voting and Collective Choice. Cambridge Univ. Press, Cambridge 1970.

B. Schweizer and A. Sklar: Probabilistic Metric Spaces. North Holland, Amsterdam 1983.

L. E. Shirland, R. R. Jesse, R. L. Thompson, and C. L. Iacovou: Determining attribute weights using mathematical programming. Omega 31 (2003), 423 437.

E. Trillas: Sobre funciones de negation en la teoria de los subconjuntos difusos.Stochastica 111-1:47-59, 1983; English version in :Advances of Fuzzy Logic Universidad de Santiago de Compostela (S. Barro et al, eds.), Santiago de Compostela 1998, pp. 31-43.

G. Walther: Granulometric smoothing. Ann. Statist. 25 (1999), 2273 2299.

R. R. Yager: On ordered averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems, Man and Cybernetics 18 (1988), 183-190.

R. R. Yager and A. Rybalov: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111-120.

L. A. Zadeh: Fuzzy Sets. Inform, and Control 8 (1965), 338-353.

H. J. Zimmermann and P. Zysno: Latent connectives in human decision making. Fuzzy Sets and Systems 4 (1980), 37-51.

Deposited On:11 Oct 2012 09:19
Last Modified:07 Feb 2014 09:33

Repository Staff Only: item control page