A method for group decision making with multi-granularity linguistic assessment information

doi:10.1016/j.ins.2007.09.007

Information Sciences

Volume 178, Issue 4, 15 February 2008, Pages 1098-1109

https://doi.org/10.1016/j.ins.2007.09.007 Get rights and content

Abstract

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.

Introduction

Group decision making (GDM) problems with linguistic information arise from a wide range of real-world situations [6], [15], [16]. In linguistic GDM analysis, firstly, experts provide their assessment information from the pre-established linguistic term sets. Then the linguistic information provided by experts is aggregated to form a collective opinion on the alternatives and the most desirable alternative(s) can be selected according to the derived collective opinion [7], [13], [19].

Most of the proposals for solving GDM problems with linguistic information have been found in literature are focused on the cases where the information provided by experts is represented in the same linguistic term set [11], [14]. However, in practical GDM problems, the experts have their different cultural, educational backgrounds, experience and knowledge. Also their decisions can be made under different circumstances. The experts maybe use linguistic term sets with different cardinalities, i.e., multi-granularity linguistic term sets, to express their individual assessment information [10]. This type of information is referred to as multi-granularity linguistic information [10], [12]. For instance, in a GDM problem of selecting R&D projects, some experts are willing to use a linguistic term set with two terms (e.g., 1: Pass and 2: Fail) while others prefer to use the one with five terms (e.g., 1: Excellent, 2: Very Good, 3: Good, 4: Pass and 5: Fail). It is necessary to point out that the linguistic term set with small cardinality is beneficial for the experts to express their clear assessment information, while the linguistic term set with large cardinality provides experts with more choices to express their exact assessment information. Therefore, the research on GDM problems with multi-granularity linguistic information is important to real applications and several methods have been proposed to solve this kind of GDM problems [10], [12].

Herrera et al. [10] investigated a fusion method based on the linguistic 2-tuple representation model to handle the multi-granularity linguistic information. In their method, firstly, the one with maximum granularity in all of the pre-established linguistic term sets was selected as the basic linguistic term set (BLTS). Then, the multi-granularity linguistic information given by experts was converted into the fuzzy sets defined in the BLTS by means of a transformation function. To obtain the collective ranking values of alternatives, these fuzzy sets were aggregated by means of the OWA aggregation operator. Subsequently, the most desirable alternative(s) was selected by using the non-dominance choice degree of alternatives. Herrera and Martinez [12] proposed another method to solve the GDM problem with multi-granularity linguistic information. They constructed linguistic hierarchy term sets and generalized transformation functions to unify the multi-granularity linguistic information into the linguistic 2-tuples. A fuzzy linguistic 2-tuple aggregation operator was used to integrate the unified information into the collective opinion and to compute the collective ranking values of alternatives. The selection of the most desirable alternative(s) was done based on the collective ranking values.

Prior studies [10], [12] have significantly advanced GDM analysis with multi-granularity linguistic information. However, unifying the multi-granularity linguistic information increases the steps of computation and the expert’s subjectivity in determining a transformation function. Current methods also neglect to consider how to narrow the gap between the collective opinion and each expert’s opinion so as to make the collective opinion reach better group consensus. This paper presents a new method to deal with the GDM problem. The motivation of presenting the method is based on the following facts: (1) The proposed method does not need to unify multi-granularity linguistic information. In this paper, the experts’ multi-granularity linguistic information is integrated and collective ranking values of alternatives are directly obtained through the linear goal programming model. Thus, the proposed method is simpler than the existing ones and can avoid the subjectivity in determining a transformation function. (2) The method makes use of the optimization model. It keeps the collective opinion as close to each expert’s opinion as possible, thus makes the final collective opinion reflect every expert’s opinion and improves the group consensus. (3) The method is applicable to multi-granularity linguistic information with both symmetrical membership function and unsymmetrical membership function.

The rest of the paper is arranged as follows. In Section 2, the GDM problem with multi-granularity linguistic information is presented. In Section 3, a goal programming model is proposed to integrate the multi-granularity linguistic information and to obtain the collective ranking values of alternatives. The ranking of alternatives is determined and the most desirable alternative(s) is selected by constructing a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives and applying a non-dominance choice degree to this fuzzy preference relation. In Section 4, an example is used to illustrate the proposed method. The last section concludes this paper.

Section snippets

Presentation of the problem

This section describes the GDM problem with multi-granularity linguistic information.

Let $S^{q} = {s_{0}^{q}, s_{1}^{q}, \dots, s_{T_{q}}^{q}}$ be the qth pre-established finite and totally ordered linguistic term set with odd cardinalities, $q = 1, \dots, p$ , where $s_{h}^{q}$ denotes the hth linguistic term of set $S^{q}$ . It is seen that $T_{q} + 1$ is the cardinality of $S^{q}$ . And it is usually required that set $S^{q}$ has the following characteristics [2], [8]:

(1)
The set is ordered: $s_{t}^{q} “ ⩾ ” s_{h}^{q}$ if $t ⩾ h$ , where “⩾” means that $s_{t}^{q}$ is preferred or indifferent to $s_{h}^{q}$ .
(2)

The proposed method

The resolution process of the GDM problem with multi-granularity linguistic information is presented in Fig. 1.

In the resolution process outlined above, after the multi-granularity linguistic information is represented in the form of fuzzy numbers, a goal programming model is constructed to assess the collective ranking values of alternatives. Then, the collective ranking values of alternatives in the form of fuzzy numbers are compared to obtain the ranking of alternatives or to select the most

Illustrative example

In this section, an example about GDM problem from Herrera et al. [10] is used to illustrate the effectiveness of the proposed method. The problem is solved by our method and the fusion method presented in [10], respectively. And then a comparison analysis between the two methods is conducted.

Suppose an investment company wants to select the best option to invest a sum of money. There are four possible alternatives to be considered:

$X_{1}$ : a car industry,
$X_{2}$ : a food company,
$X_{3}$ : a computer company,

Conclusions

This paper presents a new method to solve the GDM problem with multi-granularity linguistic information. The approach is based on a linear goal programming model to integrate the experts’ assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. An example is examined to illustrate the potential applications and effectiveness of the proposed method. Its advantages are also analyzed by comparing with the existing

Acknowledgements

This work was partly supported by the National Science Fund for Distinguished Young Scholars of China (No. 70525002), the National Natural Science Foundation of China (Nos. 70721001, 70301008 and 70371050), the Research Fund for the Doctoral Program of Higher Education, Ministry of Education, China (No. 20040145018) and the Key Laboratory of Integrated Automation of Process Industry (Northeastern University), Ministry of Education, China (No. JCLL-01-05).

The authors also wish to thank the

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A method for group decision making with multi-granularity linguistic assessment information

Abstract

Introduction

Section snippets

Presentation of the problem

The proposed method

Illustrative example

Conclusions

Acknowledgements

European Journal of Operation Research

European Journal of Operational Research

International Journal of Production Economics

Fuzzy Sets and Systems

Information Sciences

Fuzzy Sets and Systems

European Journal of Operational Research

Fuzzy Sets and Systems

European Journal of Operational Research

European Journal of Operational Research