An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges
Introduction
In the real world there are many situations in which problems must deal with vague and imprecise information that usually involves uncertainty in their definition frameworks. The use of numerical based modelling to represent such uncertain information is not always adequate. In those cases in which the uncertainty is not of probabilistic nature, it is hard to provide numerical precise information when the knowledge is vague. Often the experts that take part in this type of problems use linguistic descriptors to express their assessments regarding the uncertain knowledge they have about the problem [83], [86]. Therefore, the use of linguistic modelling in problems dealing with non-probabilistic uncertainty seems logic and has produced successful results in different fields such as: situation awareness [74], decision models [11], [15], [19], [33], [72], [85], [124], information retrieval [50], [51], [52], risk assessment [38], [69], [107], engineering evaluation [81], [83], sensory evaluation [20], [75], [77], [132], performance appraisal [25], [27], recommender systems [78], [84], [99], data mining [56], and social choice [39]. This success would not have been possible without methodologies to carry out the processes of computing with words (CW) [116], [139], [140] that implies the use of linguistic information.
Notwithstanding some methodologies for CW are based on probability [54], [61], [62], [63], the uncertainty modelled in those problems is rather related to the imprecision and vagueness of the meaning of the linguistic descriptors. Consequently other tools as Fuzzy Logic [135] and the Fuzzy Linguistic Approach [136], [137], [138] grounds the basis for different computational models for CW, such as:
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The Linguistic Computational Model Based on Membership Functions [28], [76], [95]. It is based on the fuzzy linguistic approach and makes the computations directly on the membership functions of the linguistic terms by using the Extension Principle [34], [58].
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The Linguistic Symbolic Computational Models Based on Ordinal Scales [126]. It represents the information according to the fuzzy linguistic approach and uses the ordered structure of the linguistic term set to accomplish symbolic computations in such ordered linguistic scales. Similar approaches based on this way of computing were presented in [29], [125]. It is remarkable that this model has been extensively applied to decision making processes because its easy adaptation and simplicity for decision makers [126], [128], [129].
These models follow the computational scheme depicted by Yager in [130], [131] (see Fig. 1), that points out the importance of the translation and retranslation processes in CW, likewise Mendel and Wu highlight similar processes in computing with perceptions [88], [89]. Because the former involves taking information linguistically and translates into machine manipulative format. Meanwhile the latter involves taking the results from the manipulation machine format and transforms them into linguistic information that will be understandable by human beings that is one of the main objectives of CW [90].
The previous linguistic computational models present an important weakness, because they performed the retranslation step as an approximation process to express the results in the original expression domain (initial term set) provoking a lack of accuracy [45]. To avoid such inaccuracy in the retranslation step was introduced:
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The 2-tuple Linguistic Computational Model [44]. It is a symbolic model that extends the use of indexes modifying the fuzzy linguistic approach representation by adding a parameter to the basic linguistic representation in order to improve the accuracy of the linguistic computations after the retranslation step keeping the CW scheme showed in Fig. 1 and the interpretability of the results.
A deep revision of the specialized literature in CW shows the rapid growth and applicability of the 2-tuple linguistic representation model, that has been applied to many different problems (mainly decision analysis) and extended in different ways across the various hundreds of papers that have cited the seminal paper of this model.1
Therefore, we consider that after more than ten years time that the 2-tuple linguistic representation model was presented, it would be very interesting to make an overview about this model, paying attention to the necessity and foundations of the model [44], [45], methodologies for CW in complex frameworks [36], [42], [43], [46], [47] and new linguistic computing models based on it [32], [114]. As well it will be revised the different applications and problems in which the model has been successfully applied. Eventually, we concern about the challenges that the 2-tuple linguistic representation model should face to provide satisfactory solutions to other decision analysis problems.
The paper is structured as: Section 2 provides a revision about the foundations of the 2-tuple linguistic representation model both basics and use of the model. Section 3 presents the different methodologies based on the 2-tuple linguistic model for CW in complex frameworks. New linguistic computational models based on the 2-tuple are revised in Section 4. In Section 5 a deep review of the applications in which the 2-tuple linguistic model has been applied is showed. Section 6 points out some challenges of the 2-tuple linguistic model in CW and finally the paper is concluded in Section 7.
Section snippets
2-Tuple linguistic representation model for CW
The aim of this section is to review the foundations of the 2-tuple linguistic representation model both representation and computing models and afterwards to show the use of this model on the main research branches in which it has been applied.
2-tuple based methodologies for linguistic complex frameworks
The 2-tuple linguistic representation model aimed to improve the accuracy of processes of CW in linguistic frameworks where the universe of discourse was just one linguistic term set with the terms uniform and symmetrically distributed. However, it is common that in decision making problems under uncertainty the decision framework would be more complex than a symmetrical linguistic term set, such as:
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Multi-granular linguistic information: In problems with multiple experts or multiple criteria
New linguistic computational models based on 2-tuple representation
In spite of the youth of the 2-tuple representation model, many researchers has paid attention to it both for its application to different problems and for extending the model to improve several aspects in CW. In this section we review new linguistic computational models [32], [114] based on extensions of the 2-tuple representation model and/or hybridizing it with other linguistic models.
Applications of the 2-tuple representation linguistic model
Once we have reviewed the preponderant position that the 2-tuple linguistic model plays among the different linguistic computing models for CW and its use as basis for different models in research purposes. In this section our aim is to show different applications (published in the specialized literature) based on this linguistic model.
The 2-tuple linguistic model and its extensions have been applied to a wide variety of applications, mainly based on decision making and decision analysis
Linguistic 2-tuple representation model. Challenges
The management of uncertain and vague information is always hard and complex, across this paper it has been showed that linguistic modelling is a good choice to model and manage such a type of information but it implies the accomplishment of processes of CW. The different views that exist about CW [89], [90] open many problems that might be modelled and solved by means of linguistic modelling and CW processes.
Despite the different linguistic computing models introduced in the specialized
Concluding remarks
Uncertainty usually appears in many real world problems, the use of probability can cope with it in some situations. However, when such an uncertainty is not probabilistic the use of the linguistic information has provided very successful results. There exist different models to deal with linguistic information and accomplish the processes of CW, we have paid attention to one of them, the 2-tuple linguistic model that has been widely used in many fields and applications due to its accuracy and
Acknowledgments
This paper has been partially supported by the research Projects TIN2009-08286 and Feder Fonds.
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