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Über dieses Buch

This book examines one of the more common and wide-spread methodologies to deal with uncertainty in real-world decision making problems, the computing with words paradigm, and the fuzzy linguistic approach. The 2-tuple linguistic model is the most popular methodology for computing with words (CWW), because it improves the accuracy of the linguistic computations and keeps the interpretability of the results.

The authors provide a thorough review of the specialized literature in CWW and highlight the rapid growth and applicability of the 2-tuple linguistic model. They explore the foundations and methodologies for CWW in complex frameworks and extensions. The book introduces the software FLINTSTONES that provides tools for solving linguistic decision problems based on the 2-tuple linguistic model.

Professionals and researchers working in the field of classification or fuzzy sets and systems will find The 2-tuple Linguistic Model: Computing with Words in Decision Making a valuable resource. Undergraduate and postdoctoral students studying computer science and statistics will also find this book a useful study guide.



Chapter 1. Linguistic Decision Making and Computing with Words

Decision making is a common daily life activity for human beings in which, among different choices, they choose the most suitable one for the situation by means of mental and reasoning processes. Decision theory provides a wide range of tools to deal with these problems based on deterministic and probabilistic approaches. However, the uncertainty, vagueness, and imprecision that can be involved in decision problems may not always be modelled in a probabilistic way. In such situations the use of linguistic information is quite natural and common, originating linguistic decision making (LDM). To deal with linguistic descriptors and their inherent vagueness and uncertainty, tools based on fuzzy logic and fuzzy linguistic approaches have risen to facilitate information modelling and enhance the reliability and flexibility of classical decision models. This book is devoted to the use of the 2-tuple linguistic model and its extensions in LDM; this initial chapter tries to clarify the importance of linguistic information in decision making: why is fuzzy linguistic modelling suitable and adequate for complex decision making, and how can LDM problems be solved. The necessity of carrying out computational processes with linguistic information together with the ”Computing with Words” methodology is then reviewed to establish a clear computational basis to operate linguistically in LDM problems. Eventually, a short analysis of different linguistic computational models to show their features and limitations is provided.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 2. 2-Tuple Linguistic Model

The main concepts of Computing with Words and linguistic decision making (LDM) have been reviewed and some limitations of the classical linguistic computational models dealing with linguistic information pointed out. This chapter introduces the aim, concept, representation, notation, and transformation functions needed to deal with the 2-tuple linguistic model that are the basis for developing an accurate symbolic computational model defined on this representation for Computing with Words in LDM. Several basic operators are then defined, paying special attention to the aggregation ones due to their relevance in LDM.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 3. Linguistic Approaches Based on the 2-Tuple Fuzzy Linguistic Representation Model

Linguistic modelling has been applied to decision making, among other research fields, since the beginning of the 1980s with successful and interesting results. The introduction of the 2-tuple linguistic model opened the door to a further intensive, extensive, and deeper study of the use of linguistic information and Computing with Words by using symbolic approaches in different applications, mainly in the decision-making field and related topics. Such a study has attracted the attention of many scientists whose research concerns how to improve the use of symbolic models for Computing with Words in linguistic decision making. As a result of such research some new symbolic approaches have been developed that try to improve different aspects of the 2-tuple linguistic model; several of these approaches are directly based on it and aim at overcoming some specific limitations of the 2-tuple linguistic model. This chapter presents a review of several of those symbolic approaches that are based on it and its concepts.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 4. Decision Making in Heterogeneous Context: 2-Tuple Linguistic Based Approaches

In Chapter 2 it has been stated the 2-tuple linguistic model deals with linguistic information in an accurate way in decision-making problems defined in linguistic contexts in which all experts provide their information on the same linguistic scale. However, real-world decision problems are usually defined in much more complex contexts, in which heterogeneous information with multiple linguistic scales or with different types of information is necessary for modelling the information elicited by the experts involved in the decision situation. This chapter shows several 2-tuple linguistic based approaches that have been developed to deal with those heterogeneous contexts in decision-making problems: the 2-tuple linguistic based approaches to deal with multigranular linguistic information and the 2-tuple linguistic based model to deal with nonhomogeneous information.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 5. Decision Making with Unbalanced Linguistic Information

In previous chapters the linguistic information has always been modelled by means of linguistic terms uniformly and symmetrically distributed in a linguistic term set, because it performs and adapts well to many problems. However, on some occasions the necessity of dealing with symmetrically distributed nonuniform terms in the scales arises because the problem needs preference scales in which one side of the scale has a greater granularity than the other. The managing of such a type of linguistic unbalanced scales is quite challenging for Computing with Words even more if precise, linguistic, and easily understandable results are required. This chapter describes a methodology to deal with unbalanced linguistic information that not only facilitates computation with this type of information, but also provides a fuzzy representation that guarantees precise and linguistic results by using the 2-tuple linguistic model.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 6. Dealing with Hesitant Fuzzy Linguistic Information in Decision Making

The 2-tuple linguistic model and its extensions have introduced some improvements to overcome several limitations in linguistic modeling, however, there are still some challenges to face, mainly because most linguistic models including the 2-tuple linguistic model restrict experts to using single linguistic terms to express their opinions. Sometimes due to the lack of information or knowledge about the problem, experts hesitate among several linguistic terms, and the use of only one linguistic term is not enough to represent their knowledge in a correct and accurate way. This chapter introduces the concept of hesitant fuzzy linguistic term sets which keeps the basis of the fuzzy linguistic approach and allows generating more flexible and richer linguistic expressions than single linguistic terms, hence it seems adequate to deal with experts’ hesitation in linguistic contexts. A multicriteria decision-making model based on 2-tuple linguistics that deal with comparative linguistic expressions is also introduced.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 7. 2-Tuple Linguistic Decision Based Applications

Throughout this book different theoretical concepts, models, and extensions related to the 2-tuple linguistic model illustrated by simple examples to understand their performance have been reviewed. This chapter aims at showing the important impact in practice that this model and its related tools have had in different decision applications and related areas. In order to clarify its multidisciplinary impact, they are classified into five different categories and different publications about them are reviewed.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera

Chapter 8. Flintstones: A Fuzzy Linguistic Decision Tools Enhancement Suite

Previous chapters have introduced distinct linguistic modelling approaches to different computational tools passing by several decision models for solving linguistic decision-making processes defined in different frameworks and real-world situations. However, in contrast with other decision-making models there is not much software to support and help decision makers and managers in the resolution of the decision processes in linguistic decision making. This chapter shows a fuzzy linguistic decision tool enhancement suite, called Flintstones, that provides tools for solving linguistic decision problems based on the 2-tuple linguistic model, following the Computing with Words paradigm. Such a suite is licensed under the terms of the GNU General Public License and all readers can download and extend it for their own needs. It is also remarkable that together with this suite a website has been developed that contains all the datasets of the examples used in this book except the one presented in Chapter 6 Additionally, there are some more case studies with datasets that can be used by researchers to compare their proposals with the previous ones for different linguistic decision problems.
Luis Martínez, Rosa M. Rodriguez, Francisco Herrera
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