Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets

Mohammed-Amine Abchir; Isis Truck

Kybernetika (2013)

  • Volume: 49, Issue: 1, page 164-180
  • ISSN: 0023-5954

Abstract

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In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the computations are accomplished without loss of information while the results of the decision-making processes always refer to the initial linguistic term set. They propose a fuzzy partition which distributes data on the axis by using linguistic hierarchies to manage the non-uniformity. However, the required input (especially the density around the terms) taken by their fuzzy partition algorithm may be considered as too much demanding in a real-world application, since density is not always easy to determine. Moreover, in some limit cases (especially when two terms are very closed semantically to each other), the partition doesn't comply with the data themselves, it isn't close to the reality. Therefore we propose to modify the required input, in order to offer a simpler and more faithful partition. We have added an extension to the package jFuzzyLogic and to the corresponding script language FCL. This extension supports both 2-tuple models: Herrera and Martínez' and ours. In addition to the partition algorithm, we present two aggregation algorithms: the arithmetic means and the addition. We also discuss these kinds of 2-tuple models.

How to cite

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Abchir, Mohammed-Amine, and Truck, Isis. "Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets." Kybernetika 49.1 (2013): 164-180. <http://eudml.org/doc/252485>.

@article{Abchir2013,
abstract = {In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the computations are accomplished without loss of information while the results of the decision-making processes always refer to the initial linguistic term set. They propose a fuzzy partition which distributes data on the axis by using linguistic hierarchies to manage the non-uniformity. However, the required input (especially the density around the terms) taken by their fuzzy partition algorithm may be considered as too much demanding in a real-world application, since density is not always easy to determine. Moreover, in some limit cases (especially when two terms are very closed semantically to each other), the partition doesn't comply with the data themselves, it isn't close to the reality. Therefore we propose to modify the required input, in order to offer a simpler and more faithful partition. We have added an extension to the package jFuzzyLogic and to the corresponding script language FCL. This extension supports both 2-tuple models: Herrera and Martínez' and ours. In addition to the partition algorithm, we present two aggregation algorithms: the arithmetic means and the addition. We also discuss these kinds of 2-tuple models.},
author = {Abchir, Mohammed-Amine, Truck, Isis},
journal = {Kybernetika},
keywords = {fuzzy partitioning; fuzzy linguistic 2-tuples; unbalanced linguistic term sets; linguistic aggregation; fuzzy partitioning; fuzzy linguistic 2-tuples; unbalanced linguistic term sets; linguistic aggregation},
language = {eng},
number = {1},
pages = {164-180},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets},
url = {http://eudml.org/doc/252485},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Abchir, Mohammed-Amine
AU - Truck, Isis
TI - Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 164
EP - 180
AB - In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the computations are accomplished without loss of information while the results of the decision-making processes always refer to the initial linguistic term set. They propose a fuzzy partition which distributes data on the axis by using linguistic hierarchies to manage the non-uniformity. However, the required input (especially the density around the terms) taken by their fuzzy partition algorithm may be considered as too much demanding in a real-world application, since density is not always easy to determine. Moreover, in some limit cases (especially when two terms are very closed semantically to each other), the partition doesn't comply with the data themselves, it isn't close to the reality. Therefore we propose to modify the required input, in order to offer a simpler and more faithful partition. We have added an extension to the package jFuzzyLogic and to the corresponding script language FCL. This extension supports both 2-tuple models: Herrera and Martínez' and ours. In addition to the partition algorithm, we present two aggregation algorithms: the arithmetic means and the addition. We also discuss these kinds of 2-tuple models.
LA - eng
KW - fuzzy partitioning; fuzzy linguistic 2-tuples; unbalanced linguistic term sets; linguistic aggregation; fuzzy partitioning; fuzzy linguistic 2-tuples; unbalanced linguistic term sets; linguistic aggregation
UR - http://eudml.org/doc/252485
ER -

References

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  11. Martínez, L., Ruan, Da, Herrera, F., Computing with words in decision support systems: An overview on models and applications., Internat. J. Computat. Intelligence Systems 3 (2010), 4, 382-395. 
  12. Ruspini, 10.1016/S0019-9958(69)90591-9, Inform. and Control 15 (1969), 22-32. Zbl0192.57101DOI10.1016/S0019-9958(69)90591-9
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  14. Zadeh, L. A., Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic., Fuzzy Sets and Systems 90 (1997), 2, 111-127. Zbl0988.03040MR1486256

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