A discussion on aggregation operators

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.

[1]  Gaspar Mayor Forteza,et al.  Generation of multi-dimensional aggregation functions , 1998 .

[2]  Anna Kolesárová,et al.  Triangular norm-based iterative compensatory operators , 1999, Fuzzy Sets Syst..

[3]  Jean-Luc Marichal,et al.  Characterization of some aggregation functions stable for positive linear transformations , 1999, Fuzzy Sets Syst..

[4]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

[5]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[6]  Javier Montero.  A note on Fung-Fu's theorem , 1985 .

[7]  Joan Torrens,et al.  t-Operators , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[8]  Vincenzo Cutello,et al.  On the relevance of OWA rules. , 2000 .

[9]  H. Zimmermann,et al.  Latent connectives in human decision making , 1980 .

[10]  K. S. Fu,et al.  AN AXIOMATIC APPROACH TO RATIONAL DECISION MAKING IN A FUZZY ENVIRONMENT , 1975 .

[11]  J. Montero,et al.  CLASSIFYING PIXELS BY MEANS OF FUZZY RELATIONS , 2000 .

[12]  Vincenzo Cutello,et al.  Crisp dimension theory and valued preference relations , 2004, Int. J. Gen. Syst..

[13]  Charalambos L. Iacovou,et al.  Determining attribute weights using mathematical programming , 2003 .

[14]  Toader T. Buhaescu.  UNINORM AGGREGATION OPERATORS FOR INTUITIONISTIC FUZZY SETS , 2000 .

[15]  Kai-Yuan Cai,et al.  Introduction to Fuzzy Reliability , 1996 .

[16]  Radko Mesiar,et al.  On the Relationship of Associative Compensatory operators to triangular Norms and Conorms , 1996, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[17]  J. Montero,et al.  Additive Recursive Rules , 2000 .

[18]  King-Tim Mak,et al.  Coherent Continuous Systems and the Generalized Functional Equation of Associativity , 1987, Math. Oper. Res..

[19]  Javier Montero,et al.  Spectral fuzzy classification: an application , 2002, IEEE Trans. Syst. Man Cybern. Part C.

[20]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[21]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[22]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[23]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .