### Impacto

Amo, Ana del and Montero de Juan, Francisco Javier and Molina, E.
(2001)
*Representation of consistent recursive rules.*
European journal of operational research, 130
(1).
pp. 29-53.
ISSN 0377-2217

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Official URL: http://www.sciencedirect.com/science/article/pii/S0377221700000321

## Abstract

This paper develops the recursive model for connective rules (as proposed in V. Cutello, E. Molina, J. Montero, Associativeness versus recursiveness, in: Proceedings of the 26th IEEE International Symposium on Multiple-valued Logic, Santiago de Compostela, Spain, 29-31 May, 1996, pp. 154-159; V. Cutello, E. Molina, J. Montero, Binary operators and connective rules, in: M.H. Smith, M.A. Lee, J. Keller, J. Yen (Eds.), Proceedings of NAFIPS 96, North American Fuzzy Information Processing Society, IEEE Press, Piscataway, NJ, 1996, pp. 46-49), where a particular solution in the Ordered Weighted Averaging (OWA) context (see V. Cutello, J. Montero, Recursive families of OWA operators, in: P.P. Bonissone (Ed.), Proceedings of the Third IEEE Conference on Fuzzy Systems, IEEE Press, Piscataway, NJ, 1994, pp. 1137-1141; V. Cutello, J. Montero, Recursive connective rules, International Journal of Intelligent Systems, to appear) was translated into a more general framework. In this paper, some families of solutions for the key recursive equation are obtained, based upon the general associativity equation as solved by K. Mak (Coherent continuous systems and the generalized functional equation of associativity, Mathematics of Operations Research 12 (1987) 597-625). A context for the representation of families of binary connectives is given, allowing the characterization of key families of connective rules. (C) 2001 Elsevier Science B.V. All rights reserved.

Item Type: | Article |
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Uncontrolled Keywords: | Fuzzy sets; Fuzzy connectives; Connective rules; Recursiveness; Associativity |

Subjects: | Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 16779 |

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Deposited On: | 22 Oct 2012 10:15 |

Last Modified: | 07 Feb 2014 09:35 |

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