Bustince, H. and Montero de Juan, Francisco Javier and Mesiar, R.
(2009)
*Migrativity of aggregation functions.*
Fuzzy Sets and Systems, 160
(6).
pp. 799-777.
ISSN 0165-0114

PDF
Restricted to Repository staff only until 2020. 179kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0165011408004600

## Abstract

We introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are no t-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative t-norm, as already shown by other authors) and that the only migrative idempotent aggregation function is the geometric mean. The k-Lipschitz migrative aggregation functions are also characterized and the product is shown to be the only 1-Lipschitz migrative aggregation function. Similarly, it is the only associative migrative aggregation function possessing a neutral element. Finally, the associativity and bisymmetry of migrative aggregation functions are discussed.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Aggregation functions; Migrativity; Associativity; Bisymmetry; T-norms; Uninorms; Nullnorms |

Subjects: | Sciences > Computer science > Artificial intelligence |

ID Code: | 16182 |

References: | C. Alsina, M.J. Frank, B. Schweizer, Associative Functions: Triangular Norms and Copulas, World Scientific, Hackensack, NJ, 2006. A. Amo, J. Montero, E. Molina, Representation of consistent recursive rules, Europ. J. Oper. Res. 130 (2001) 29–53. G. Beliakov, A. Pradera, T. Calvo (Eds.), Aggregation Functions: A Guide for Practitioners, Springer, Berlin, 2007. H. Bustince, P. Burillo, F. Soria, Automorphisms, negations and implication operators, Fuzzy Sets and Systems 134 (2003) 209–229. T. Calvo, B. De Baets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets and Systems 120 (2001) 385–394. T. Calvo, A. Kolesárová, M. Komorníková, R. Mesiar, Aggregation operators: properties, classes and construction methods, in: T. Calvo, G. Mayor, R. Mesiar (Eds.), Aggregation Operators New Trends and Applications, Physica-Verlag, Heidelberg, 2002, pp. 3–104. V. Cutello, J. Montero, Recursive connective rules, Internat. J. Intell. Systems 14 (1999) 3–20. B. De Baets, Uninorms: the known classes, in: D. Ruan, H.A. Abderrahim, P. D’hondt, E.E. Kerre (Eds.), Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry, World Scientific, Singapore, 1998, pp. 21–28. B. De Baets, Idempotent uninorms, Europ. J. Oper. Res. 118 (1999) 631–642. D. Dubois, W. Ostasiewicz, H. Prade, Fuzzy Sets, history and basic notions, in: D. Dubois, H. Prade (Eds.), Fundamentals of Fuzzy Sets, Kluwer, Boston, MA, 2000, pp. 21–124. F. Durante, P. Sarkoci, A note on the convex combinations of triangular norms, Fuzzy Sets and Systems 159 (2008) 77–80. J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht, 1994. J. Fodor, I.J. Rudas, On continuous triangular norms that are migrative, Fuzzy Sets and Systems 158 (2007) 1692–1697. D. Gómez, J. Montero, A discussion on aggregation operators, Kybernetika 40 (2004) 107–120. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000. G.J. Klir, T.A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall, Englewood Cliffs, NJ, 1988. R. Mesiar, V. Novák, Open problems from the 2nd International Conference of fuzzy sets theory and its applications, Fuzzy Sets and Systems 81 (1996) 185–190. J. Montero, D. Gómez, S. Muñoz, Fuzzy information representation for decision aiding, in: Proc. of the IPMU Conference, Málaga, Spain, June 22–27, 2008. J. Montero, V. López, D. Gómez, The role of fuzziness in decision making, in: D. Ruan et al. (Eds.), Fuzzy Logic: A Spectrum of Applied and Theoretical Issues, Springer, Berlin, 2007, pp. 337–349 B. Roy, Decision sciences or decision aid sciences, Europ. J. Oper. Res. 66 (1993) 184–203. B. Schweizerd, A. Sklar, Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983; Dover Publications, Mineola, NY, 2006. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996) 111–120 |

Deposited On: | 11 Sep 2012 07:43 |

Last Modified: | 06 Feb 2014 10:39 |

Repository Staff Only: item control page