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

PDF
Restricted to Repository staff only until 2020. 210kB |

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 |
---|---|

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

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

ID Code: | 16779 |

References: | J. Aczel, Lectures on Functional Equations and their Applications, Academic Press, New York, 1966. 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. 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. H. Dyckoff, Basic concepts for a theory of evaluation: hierarchical aggregation via autodistributive connectives in fuzzy set theory,European Journal of Operational Research 20 (1985) 221-233. H. Dyckoff, W. Pedrycz, Generalized means as model of compensative connectives, Fuzzy Sets and Systems 14 (1984) 143-154. J. Dombi, Basic concepts for a theory of evaluation: the aggregative operator, European Journal of Operational Research 10 (1982) 282-293. J. Dombi, A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets and Systems 8 (1982) 149-163. J.C. Fodor, J.L. Marichal, M. Roubens, Characterization of the ordered weighted averaging operators, IEEE Transactions of Fuzzy Systems 3 (1995) 236±240 Prepublication 93.011. J.C. Fodor, M. Roubens, Fuzzy Preference Modelling and Multi-criteria Decision Support, Kluwer, Dordrecht, 1994. J.C. Fodor, R.R. Yager, A. Rybalov, Structure of uninorms, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 (1997) 411-427. J.C. Fodor, S. Jenei, On reversible triangular norms, Fuzzy Sets and Systems 104 (1999) 43-51. G.H. Haardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge UP, 1954. S. Jenei, New family of triangular norms via contrapositive symmetrization of residuated implications, Fuzzy Sets and Systems 110 (2000) 157±174. T.C. Koopmans, Representation of preference ordering with independent components of consumption, in: C.B. McGuire, R. Radner (Eds.), Decision and Organization, North-Holland, Amsterdam, 1972, 57-78 (2nd edition by the University of Minnesota Press, 1986). K.T. Mak, Coherent continuous systems and the generalized functional equation of associativity, Mathematics of Operations Research 12 (1987) 597-625. J.L. Marichal, P. Mathonet, E. Tousset, Characterization of some aggregation functions stable for positive transformations,Fuzzy Sets and Systems 102 (1999) 293-314. M. Mas, G. Mayor, J. Suñer, J. Torrens, Generation of multi-dimensional aggregation functions, Mathware and Soft Computing 5 (1998) 233-242. J. Montero, J. Tejada, V. Cutello, A general model for deriving preference structures from data, European Journal of Operational Research 98 (1997) 98-110. R.R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics 18 (1988) 183-190. R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems 59 (1993) 125-148. R.R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996) 111-120. R.R. Yager, Fusion of ordinal information using weighted median aggregation, International Journal of Approximate Reasoning 18 (1998) 35-52. |

Deposited On: | 22 Oct 2012 10:15 |

Last Modified: | 07 Feb 2014 09:35 |

Repository Staff Only: item control page