# ON THE ABSOLUTE VALUE OF TRAPEZOIDAL FUZZY NUMBERS AND THE MANHATTAN DISTANCE OF FUZZY VECTORS

### Julio Rojas-Mora, Jaime Gil-Lafuente, Didier Josselin

#### 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.

#### References

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#### Paper Citation

#### in Harvard Style

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 - Volume 1: FCTA, (IJCCI 2011)* ISBN 978-989-8425-83-6, pages 399-406. DOI: 10.5220/0003674203990406

#### in Bibtex Style

@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 - Volume 1: FCTA, (IJCCI 2011)},

year={2011},

pages={399-406},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003674203990406},

isbn={978-989-8425-83-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2011)

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