On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends

doi:10.1016/j.knosys.2014.11.001

Knowledge-Based Systems

Volume 74, January 2015, Pages 49-60

https://doi.org/10.1016/j.knosys.2014.11.001 Get rights and content

Abstract

The multi-granular fuzzy linguistic modeling allows the use of several linguistic term sets in fuzzy linguistic modeling. This is quite useful when the problem involves several people with different knowledge levels since they could describe each item with different precision and they could need more than one linguistic term set. Multi-granular fuzzy linguistic modeling has been frequently used in group decision making field due to its capability of allowing each expert to express his/her preferences using his/her own linguistic term set. The aim of this research is to provide insights about the evolution of multi-granular fuzzy linguistic modeling approaches during the last years and discuss their drawbacks and advantages. A systematic literature review is proposed to achieve this goal. Additionally, some possible approaches that could improve the current multi-granular linguistic methodologies are presented.

Introduction

Decision making is a process that all humans carry out many times in their daily activities and it consists in choosing, among several possible actions, the one that is considered to give better profit. An important part of the decision making process is the way that experts express their preferences about a set of possible alternatives. The chosen method for the recollection and storage of the expert’s information is vital because, if it is not intuitive for them, they will not be able to express themselves correctly. In such a case, the decision making process would be hindered. Linguistic modeling and multi-granular FLM methods can be used in order to solve this problem.

The fuzzy linguistic approach proposed by Zadeh in 1975 [60], [61], [62] has been used satisfactorily to represent linguistic information during the last 40 years. In the current literature, it is possible to find two kinds of fuzzy linguistic approaches in order to represent linguistic information [15], [16]: traditional fuzzy linguistic approach and ordinal fuzzy linguistic approach. The former is more classical and is based on the membership functions associated to each label [60], [61], [62], while the latter is based on the symbolic ordinal representation of the labels [2], [19], [28], [45]. The symbolic approximation approach has awakened high interest among the scientific community because of its simplicity and application possibilities [14], [36], [40], [44], [46].

In some environments, using a unique Linguistic Term Set (LTS) is not enough to give a clear representation of the information. It is very important to use an adequate number of labels to represent each concept because, if the granularity is too low, then loss of precision is produced. On the other hand, if granularity is too high, then too much information is kept in each LTS and to choose the precise label that best resembles the item that is being described could become a tiresome task. In such cases, the use of several LTSs with different granularities and shapes, becomes essential. Thus, a multi-granular linguistic context should be used, i.e., several LTS should be used in order to represent the linguistic information [17]. The multi-granular fuzzy linguistic modeling (FLM) is appropriate in cases where several information providers need different criteria to express their preferences. For example, this could happen when they have different knowledge levels and need different expression linguistic domains with a different granularity and/or semantics. Multi-granular FLM has been applied successfully in areas such as information retrieval [20], [21], recommender systems [27], [43], consensus [5], [31], web quality [22], [23] and decision making [17], [25].

The aim of this paper is to show a comprehensive presentation of the state of the art of all known multi-granular FLM approaches, with an in-depth analysis of the respective problems and solutions as well as more relevant applications. Furthermore, in order to give some advice of how the described methods could be improved, new trends and challenges of multi-granular FLM are going to be discussed. From this viewpoint, this paper reports the results of a systematic literature review of researches published in international journals since 2000, taking into account their importance and impact in nowadays published methods. Methods selected after carrying out the systematic review process have been classified into six different categories:

•
Traditional multi-granular FLM based on fuzzy membership functions: Methods classified in this category use the semantics associated to each label to carry out the operations among elements of different LTSs [25], [64].
•
Ordinal multi-granular FLM based on a basic Linguistic Term Set (LTS): All the labels belonging to different LTSs are uniformed by expressing them using a unique LTS called Basic Linguistic Term Set (BLTS) and working on this special linguistic term set the required operations are carried out [9], [17], [56].
•
Ordinal multi-granular FLM based on 2-tuple FLM: In this category, methods use the 2-tuple FLM and its properties [18] to manage the multi-granular linguistic information [13], [19], [63].
•
Ordinal multi-granular FLM based on hierarchical trees: The multi-granular linguistic information is managed using the concept of hierarchical trees [24].
•
Multi-granular FLM based on qualitative description spaces: This method uses the concept of generalized description space to model and manage the multi-granular linguistic information [42].
•
Ordinal multi-granular FLM based on discrete fuzzy numbers: Discrete fuzzy numbers mathematical environment [49] is used to deal with the multi-granular linguistic information [30].

This paper is organized as follows. Section 2 presents the Preliminaries, i.e., the basis of multi-granular FLM and the strategy followed to develop the systematic review. In Section 3, different multi-granular fuzzy linguistic approaches are described. In Section 4, a comparison among those multi-granular fuzzy linguistic approaches is presented and future research lines are discussed. Finally, some conclusions are pointed out.

Section snippets

Preliminaries

This section presents some basic information about multi-granular FLM and Group Decision Making (GDM) problems. Moreover, the chosen strategy to develop a systematic (organized, efficient and accurate) literature review is described.

Analysis of multi-granular FLM methods

In this section, the main primary studies about multi-granular linguistic approaches are described, by showing their performance, characteristics and some examples of application. As mentioned in the introduction, the multi-granular linguistic approaches are organized into six different methodologies:

•
Traditional multi-granular FLM based on fuzzy membership functions.
•
Ordinal multi-granular FLM based on a basic linguistic term set.
•
Ordinal multi-granular FLM based on 2-tuple FLM.
•
Ordinal

Discussion and future trends

All the presented methods have their own advantages and drawbacks, that is, some work better in certain environments than others. Therefore, choosing the best approach in each situation is critical for obtaining good quality results. In this section, a discussion on the different fuzzy multi-granular modelings is presented in order to provide the user a brief advice of what method should be chosen depending on the problem and the quality of results that the user expects to obtain.

Conclusions

Using multi-granular information can be very useful, especially in environments where several people are involved in the resolution of the problem and/or several items have to be described. GDM is a clear example of this type of environment: several experts that do not have the same knowledge about the decision problem have to choose among several alternatives. In this paper, several multi-granular linguistic approaches have been revised. Afterwards, those approaches have been discussed in

Acknowledgements

This paper has been developed with the financing of FEDER funds in FUZZYLING-II Project TIN2010-17876, TIN2013-40658-P and Andalusian Excellence Projects TIC-05299 and TIC-5991.

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On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends

Abstract

Introduction

Section snippets

Preliminaries

Analysis of multi-granular FLM methods

Discussion and future trends

Conclusions

Acknowledgements

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