FLINTSTONES software tool that implements the 2-tuple linguistic model to solve linguistic decision making problems under uncertainty and its extensions to deal with complex frameworks such as multi-granular linguistic frameworks, heterogeneous frameworks and unbalanced linguistic frameworks.
A detail description of the theoretical aspects of the FLINTSTONES software tool is shown in the following sections:
- Linguistic decision making problems
- Computing with words paradigm
- 2-tuple linguistic model
- Extensions for complex framworks
Decision making processes are one of the most frequent mankind activities in daily life. In order to solve decision making problems, usually, human beings, experts, provide either their knowledge or assessments about a set of different alternatives in a given activity to make a decision by means of reasoning processes
When the decision making problem are defined under uncertainty that has a non-probabilistic nature, experts feel more comfortable providing their knowledge by using linguistic terms. The fuzzy logic and fuzzy linguistic approach provide tools to model and manage such an uncertainty by means of linguistic variables, providing reliable and successful results.
The use of linguistic information involves the need to operate with linguistic variables. The Computing with Words (CWW) is a paradigm based on a procedure that emulates human cognitive processes to make reasoning processes and decisions in environments of uncertainty and imprecision. In this paradigm the objects of computations are words or sentences from a natural language in order to obtain results in the original linguistic expression domain. To do so, a translation phase and a retranslation phase are included in such paradigm.
The 2-tuple linguistic model follows the computing with words paradigm. This model provides precision, simplicity and interpretability in the computations with a linguistic term set when the linguistic term set have an odd value of granularity and whose membership functions are triangular-shaped, symmetrical and uniformly distributed in the unit interval.
The 2-tuple linguistic representation model represents the information by means of a pair of values (s,alpha), where s is a linguistic term with syntax and semantics, and alpha is a numerical value assessed in [−0.5,0.5) that represents the value of the symbolic translation.
Therefore, alpha supports the difference of information between a counting of information assessed in the interval of granularity [0,g] of the linguistic terms set and the closest value in [0,g] which indicates the index of the closest linguistic term in the linguistic terms set.
The 2-tuple linguistic representation model has a linguistic computational model associated in order to accomplish CWW processes in a precise way.
This representation model was proposed by Herrera and Martínez in the following paper:
- F. Herrera, L. Martínez, A 2-tuple Fuzzy Linguistic Representation Model for Computing with Words. IEEE Transactions on Fuzzy Systems, vol. 8, issue 6, pp. 746-752, 2000.
Decision making situations under uncertainty can present complex frameworks (multi-granular linguistic, heterogeneous, unbalanced linguistic) that need more than a linguistic domain to model all preferences involved in the decision problem. In such contexts, the extensions of the 2-tuple linguistic model provide methodologies to perform processes of CWW in these frameworks, obtaining satisfactory results in linguistic decision problems. Such complex frameworks are briefly detailed below.
- Heterogeneous frameworks: Decision problems where each expert may express his/her assessments in different expression domains, depending on the level of knowledge, experience or the nature of criteria that characterized the set of alternatives. Therefore, the assessments are expressed with non-homogeneous information such as, numerical, interval or linguistic. To deal with these frameworks, a CWW methodologies based on the 2-tuple linguistic model a methodology was presented in the following paper:
- F. Herrera, L. Martínez, P.J. Sánchez, Managing non-homogeneous information in group decision making. European Journal of Operational Research, vol. 166, issue 1, pp. 115-132, 2005.
- Multi-granular frameworks: Decision problems with multiple experts or multiple criteria in which appear linguistic information assessed in
multiple linguistic term sets with different granularity. Therefore, the assessments of the problem are represented in multiple linguistic scales.Three CWW methodologies based on the 2-tuple linguistic model have been proposed to deal with multiple linguistic scalesthat are indicated below.
- F. Herrera, E. Herrera-Viedma, L. Martínez, A Fusion Approach for Managing Multi-Granularity Linguistic Term Sets in Decision Making. Fuzzy Sets and Systems, vol. 114, issue 1, pp. 43-58, 2000.
- F. Herrera, L. Martínez, A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in Multiexpert Decision-Making. IEEE Transactions on Systems, Man and Cybernetics. Part B: Cybernetics, vol. 31, issue 2, pp. 227-234, 2001.
- M. Espinilla, J. Liu, L. Martínez, An Extended Hierarchical Linguistic Model for Decision-Making Problems. Computational Intelligence, vol. 27, issue 3, pp. 489-512, 2011.
- Unbalanced linguistic frameworks: Decision problems in which it is necessary to assess preferences with a greater granularity on a side of the linguistic scale than on another one. Hence, linguistic terms of the scale are not uniform either symmetrically distributed. Therefore, experts express their assessments in an unbalanced linguistic scale. In the following paper was presented a methodology based on linguistic hierarchies to deal with unbalanced frameworks.
- F. Herrera, E. Herrera-Viedma, L. Martínez, A Fuzzy Linguistic Methodology To Deal With Unbalanced Linguistic Term Sets. IEEE Transactions on Fuzzy Systems, vol. 16, issue 2, pp. 354-370, 200
The 2-tuple linguistic model has been widely used to operate with linguistic information in decision problems due to the fact that provides linguistic results that are easy to understand for human beings. Furthermore, the existence of different extensions based on 2-tuple linguistic model to accomplish processes of
computing with words in complex decision frameworks have also implied its use in wide variety of applications. A deep revision of the 2-tuple linguistic representation model, its extensions and applicability can be found in the following paper:
- L. Martínez, F. Herrera, An overview on the 2-tuple linguistic model for Computing with Words in Decision Making: Extensions, applications and challenges. Information Sciences, vol. 207, issue 1, pp. 1-18, 2012.