# Abstract:

In the domain of \emph{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$\ldots$ by \emph{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.

# Keywords:

fuzzy partitioning, fuzzy linguistic 2-tuples, unbalanced linguistic term sets, linguistic aggregation

# Classification:

03B52, 03E72, 68T30, 90C70

# References:

1. M.-A. Abchir: A jFuzzyLogic Extension to Deal With Unbalanced Linguistic Term Sets. Book of Abstracts 2011, pp. 53-54.   CrossRef
2. M.-A. Abchir and I. Truck: Towards a new fuzzy linguistic preference modeling approach for geolocation applications. In: Proc. EUROFUSE Workshop on Fuzzy Methods for Knowledge-Based Systems 2011, pp. 413-424.   CrossRef
3. V. Ambriola and V. Gervasi: Processing natural language requirements. In: International Conference on Automated Software Engineering, Los Alamitos 1997. IEEE Computer Society, p. 36.   CrossRef
4. P. Booth: An Introduction to Human-Computer Interaction. Lawrence Erlbaum Associates, Publishers, New Jersey 1989.   CrossRef
5. P. Ch\^atel, I. Truck and J. Malenfant: LCP-nets: A linguistic approach for non-functional preferences in a semantic SOA environment. J. Universal Computer Sci. 1 (2010), 198-217.   CrossRef
6. B. Costa: Multiple criteria decision aid: An overview. In: Readings in Multiple Criteria Decision Aid, Springer-Verlag, 1990, pp. 3-14.   CrossRef
7. F. Herrera, S. Alonso, F. Chiclana and E. Herrera-Viedma: Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim. Decision Making 8 (2009), 337-364.   CrossRef
8. F. Herrera, E. Herrera-Viedma and L. Martínez: A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans. Fuzzy Systems 16 (2008), 2, 354-370.   CrossRef
9. F. Herrera and L. Martínez: A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Systems 8 (2000), 6, 746-752.   CrossRef
10. F. Herrera and L. Martínez: A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision making. IEEE Trans. Systems, Man Cybernet. Part B: Cybernetics 31 (2001), 2, 227-234.   CrossRef
11. L. Martínez, Da Ruan and F. Herrera: Computing with words in decision support systems: An overview on models and applications. Internat. J. Computat. Intelligence Systems 3 (2010), 4, 382-395.   CrossRef
12. Ruspini: A new approach to clustering. Inform. and Control 15 (1969), 22-32.   CrossRef
13. L. A. Zadeh: The concept of a linguistic variable and its application to approximate reasoning, I, II and III. In: Inf. Sci. 8 (1975).   CrossRef
14. L. A. Zadeh: 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.   CrossRef