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Garmendia, L. and Salvador, A and Montero, Javier
(2009)
*Computing a T-transitive lower approximation or opening of a proximity relation.*
Fuzzy Sets and Systems, 160
(14).
pp. 2097-2015.
ISSN 0165-0114

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011409000554

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http://www.sciencedirect.com | Publisher |

## Abstract

Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the higher the number of elicitations, the more probable is inconsistency. This is mostly the case within a fuzzy framework, even when the number of alternatives or objects to be classified is relatively small. In this paper, we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy

relation, T being any left-continuous t-norm. The computed approximation we propose will have O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors’ knowledge, there is no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.

Item Type: | Article |
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Uncontrolled Keywords: | Fuzzy relation; Fuzzy proximity relation; T-transitive relation; fuzzy similarity; T-indistinguishability; T-transitive lower approximation; T-transitive opening |

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

ID Code: | 16156 |

Deposited On: | 11 Sep 2012 08:21 |

Last Modified: | 23 Aug 2018 06:55 |

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