On multi-granular fuzzy linguistic modeling in group decision making problems: A systematic review and future trends
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:
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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].
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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].
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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].
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Ordinal multi-granular FLM based on hierarchical trees: The multi-granular linguistic information is managed using the concept of hierarchical trees [24].
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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].
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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:
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Traditional multi-granular FLM based on fuzzy membership functions.
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Ordinal multi-granular FLM based on a basic linguistic term set.
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Ordinal multi-granular FLM based on 2-tuple FLM.
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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.
In
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.
References (64)
- et al.
Lessons from applying the systematic literature review process within the software engineering domain
J. Syst. Softw.
(2007) - et al.
A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts
Eur. J. Oper. Res.
(2013) - et al.
An approximate approach for ranking fuzzy numbers based on left and right dominance
Comput. Math. Appl.
(2001) - et al.
Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets
Expert Syst. Appl.
(2010) - et al.
On the fusion of multi-granularity linguistic label sets in group decision making
Comput. Ind. Eng.
(2006) - et al.
Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations
Eur. J. Oper. Res.
(2007) - et al.
Ranking fuzzy numbers in the setting of possibility theory
Inform. Sci.
(1983) - et al.
A linguistic decision support model for QoS priorities in networking
Knowl.-Based Syst.
(2012) - et al.
Linguistic decision analysis: steps for solving decision problems under linguistic information
Fuzzy Sets Syst.
(2000) - et al.
A fusion approach for managing multi-granularity linguistic term sets in decision making
Fuzzy Sets Syst.
(2000)
Incorporating filtering techniques in a fuzzy linguistic multi-agent model for information gathering on the web
Fuzzy Sets Syst.
A fuzzy linguistic model to evaluate the quality of web sites that store XML documents
Int. J. Approx. Reason.
A method for group decision making with multi-granularity linguistic assessment information
Inform. Sci.
An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges
Inform. Sci.
Kernel aggregation functions on finite scales. Constructions from their marginals
Fuzzy Sets Syst.
A new linguistic computational model based on discrete fuzzy numbers for computing with words
Inform. Sci.
Some properties of fuzzy sets of type 2
Inform. Contr.
Decision-making with a fuzzy preference relation
Fuzzy Sets Syst.
A linguistic aggregation operator with three kinds of weights for nuclear safeguards evaluation
Knowl.-Based Syst.
A hybrid recommender system for the selective dissemination of research resources in a technology transfer office
Inform. Sci.
A google wave-based fuzzy recommender system to disseminate information in university digital libraries 2.0
Inform. Sci.
A hierarchical model of a linguistic variable
Inform. Sci.
A consensus model for group decision making problems with linguistic interval fuzzy preference relations
Expert Syst. Appl.
A quality based recommender system to disseminate information in a university digital library
Inform. Sci.
Aggregation of subjective evaluations based on discrete fuzzy numbers
Fuzzy Sets Syst.
Canonical representations of discrete fuzzy numbers
Fuzzy Sets Syst.
Hesitant fuzzy prioritized operators and their application to multiple attribute decision making
Knowl.-Based Syst.
Hesitant fuzzy information aggregation in decision making
Int. J. Approx. Reason.
Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment
Inform. Sci.
An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations
Decis. Support Syst.
The concept of a linguistic variable and its application to approximate reasoning – I
Inform. Sci.
The concept of a linguistic variable and its application to approximate reasoning – II
Inform. Sci.
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