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Authors: Julio Rojas-Mora 1 ; Jaime Gil-Lafuente 2 and Didier Josselin 1

Affiliations: 1 Université d’Avignon (UAPV), France ; 2 University of Barcelona, Spain

Keyword(s): Fuzzy sets, Manhattan distance, Absolute value.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Computational Intelligence ; Fuzzy Systems ; Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic ; Soft Computing

Abstract: The computation of the Manhattan distance for fuzzy vectors composed of trapezoidal fuzzy numbers (TrFN) requires the application of the absolute value to the differences between components. The membership function of the absolute value of a fuzzy number has been defined by Dubois and Prade as well as by Chen and Wang. The first one only removes the negative values of the fuzzy number, increasing its expected value. Conversely, Chen and Wang’s definition maintains the expected value, but can produce a TrFN with negative values. In this paper, we present the “positive correction” of the absolute value, a method to remove the negative values of a TrFN while maintaining its expected value. This operation also complies with a logic principle of any uncertain distance: reducing the distance should also reduce its uncertainty.

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Paper citation in several formats:
Rojas-Mora, J.; Gil-Lafuente, J. and Josselin, D. (2011). ON THE ABSOLUTE VALUE OF TRAPEZOIDAL FUZZY NUMBERS AND THE MANHATTAN DISTANCE OF FUZZY VECTORS. In Proceedings of the International Conference on Evolutionary Computation Theory and Applications (IJCCI 2011) - FCTA; ISBN 978-989-8425-83-6, SciTePress, pages 399-406. DOI: 10.5220/0003674203990406

@conference{fcta11,
author={Julio Rojas{-}Mora. and Jaime Gil{-}Lafuente. and Didier Josselin.},
title={ON THE ABSOLUTE VALUE OF TRAPEZOIDAL FUZZY NUMBERS AND THE MANHATTAN DISTANCE OF FUZZY VECTORS},
booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications (IJCCI 2011) - FCTA},
year={2011},
pages={399-406},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003674203990406},
isbn={978-989-8425-83-6},
}

TY - CONF

JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications (IJCCI 2011) - FCTA
TI - ON THE ABSOLUTE VALUE OF TRAPEZOIDAL FUZZY NUMBERS AND THE MANHATTAN DISTANCE OF FUZZY VECTORS
SN - 978-989-8425-83-6
AU - Rojas-Mora, J.
AU - Gil-Lafuente, J.
AU - Josselin, D.
PY - 2011
SP - 399
EP - 406
DO - 10.5220/0003674203990406
PB - SciTePress

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