In this paper, we investigate green supplier evaluation and selection problems within the interval 2-tuple linguistic environment. Based on the operational laws and comparison rule of interval 2-tuple linguistic variables, we develop some new aggregation operators, such as the interval 2-tuple hybrid averaging (ITHA) operator, the interval 2-tuple ordered weighted averaging-weighted averaging (ITOWAWA) operator and the interval 2-tuple hybrid geometric (ITHG) operator. Then, an approach for green supplier evaluation and selection under the context of interval 2-tuple linguistic variables is proposed based on the developed interval 2-tuple linguistic hybrid aggregation operators. Finally, a practical application to the green supplier selection problem of an automobile manufacturer is presented to reveal the potentiality and aptness of the proposed green supplier selection approach. According to the findings, the supplier number ‘five’ got the highest rank, out of the five alternative green suppliers. The approach proposed in this paper may help managers and business professionals to evaluate and select the optimal green supplier by considering the importance degrees of both the given arguments and their ordered positions. Furthermore, it is able to take different scenarios into account and provide a more complete picture to the decision maker by using different hybrid aggregation operators.
Supply chain management (SCM) is a process of systematizing and amalgamating diverse activities, starting from customers’ order to end product delivery in a well-organized manner (Kahraman
Because green supplier is located upstream of an entire supply chain, it can improve the compatibility of a supply chain effectively and impact the environmental performance of a manufacturer greatly. Green supplier selection can be considered as a kind of multiple criteria decision making (MCDM) problem that involves many qualitative and quantitative evaluation criteria, such as resource consumption, green image, green competencies, and product life cycle cost (Cao
To aggregate the interval 2-tuple linguistic information in the decision making process, Zhang (
Against the above background, the intent of this paper is to develop a green supplier evaluation and selection framework based on interval 2-tuple linguistic hybrid aggregation operators to evaluate and determine the most appropriate green supplier in the presence of uncertainty. This research contributes to the literature in the following three dimensions. First, we propose some new aggregation operators, i.e. the interval 2-tuple hybrid averaging (ITHA) operator, the interval 2-tuple ordered weighted averaging-weighted averaging (ITOWAWA) operator and the interval 2-tuple hybrid geometric (ITHG) operator, by considering the weights of the given arguments and their ordered positions. Second, a decision making approach is introduced for handling the green supplier selection problems with interval 2-tuple linguistic information. Third, we utilize an application example in an automobile manufacturing company to show the feasibility and practicality of the proposed green supplier selection approach. Towards this end, the remaining part of this paper is organized as follows: Section
In this section, we mainly review the related literature on green supplier selection methods and interval 2-tuple linguistic aggregation operators.
In recent years, researchers have presented many decision making approaches and techniques for the selection of optimal green suppliers (Mardani
In recent years, many interval 2-tuple linguistic aggregation operators have been developed since information aggregation plays a large role in the decision making process. For instance, Shan
The literature review above shows that a variety of methods have been proposed by researchers to resolve the issue of evaluating and ranking green suppliers. However, little attention has been paid to the interval 2-tuple linguistic method for assessing suppliers’ green performance in the presence of uncertainty. The interval 2-tuple linguistic ELECTRE II (Wan
In this section, some basic definitions and notations concerning 2-tuple linguistic variables and interval 2-tuple linguistic variables are presented.
Linguistic variables are able to deal with the circumstances which are too complex or too ill-defined to be handled using the traditional quantitative expressions (Zadeh,
(1) Negation operator:
(2) The set is ordered:
(3) Max operator:
The 2-tuple linguistic method was firstly proposed in Herrera and Martínez (
Let
Let
Based on the definitions of Tai and Chen (
Let
Given any three interval 2-tuples
(1)
(2)
(3)
(4)
The comparison of linguistic information represented by interval 2-tuples is implemented on the basis of the degree of possibility of interval 2-tuple linguistic variables.
Let
From Definition
To rank
This section develops some interval 2-tuple linguistic hybrid aggregation operators including the interval 2-tuple hybrid averaging (ITHA) operator, the interval 2-tuple ordered weighted averaging-weighted averaging (ITOWAWA) operator and the interval 2-tuple hybrid geometric (ITHG) operator.
Let
Let
The ITWA operator weights only the input interval 2-tuple arguments, whereas the ITOWA operator weights only the ordered positions of the interval 2-tuple arguments. Therefore, we can see that weights denote different features in the ITWA and the ITOWA operators. However, both the operators only take one of them into account. To solve this drawback, an ITHA operator is proposed in the following part.
Let
Assume
The ITHA operator arrives to a unification between the ITWA and the ITOWA operators because both concepts are included in the formulation as particular cases. However, the model can unify them but it cannot consider how relevant these concepts are in a specific problem considered. For example, in some problems we may prefer to give more importance to the ITOWA operator because we believe that it is more relevant and vice versa. To overcome this issue, in the following we present an ITOWAWA operator.
Let
It is worthwhile to point out that we can formulate the ITOWAWA operator by separating the part that strictly affects the ITOWA operator and the part that affects the ITWA operator.
Let
The key benefit of the ITOWAWA operator is that it combines the ITOWA and the ITWA operators considering the importance degree of each concept in the formulation. Therefore, in the real application, it is possible to give more or less importance to the ITOWA operator or the ITWA operator depending on our interests on the problem analysed.
Assume
From the above computations, it can be observed that the same results are derived with both methods.
Let
Let
From Definitions
Let
Assume
In this section, we investigate green supplier selection problems based on the proposed interval 2-tuple linguistic hybrid aggregation operators, where the criteria weights take the form of real numbers and criteria values take the form of interval 2-tuple linguistic variables.
Suppose that a green supplier selection problem has
In the following, we apply the developed interval 2-tuple linguistic hybrid aggregation operators to address the green supplier selection problems in the interval 2-tuple linguistic context. The method involves the following steps:
Suppose that
A certain rating such as
An interval grade, e.g.
If a decision maker is not willing to or cannot provide a judgement for an alternative concerning the criterion under consideration, then the assessment could be anywhere between
We first compare each
In what follows, a practical example is presented to illustrate the developed green supplier selection model. A comparison is also made between the results of the proposed approach and some extant methods to validate the proposed approach.
With the increased awareness of environmental issues worldwide, green SCM has played an important role in marketing economy and has become the hottest research topic in modern enterprise production operation management. Green supplier evaluation and selection are one of the most important problems in green SCM, which directly impact on a manufacturer’s environment performance. Suppose that an automobile manufacturing enterprise needs to select the best green supplier for purchasing the key components of its new automobile equipment. After a preliminary screening, five potential automobile equipment suppliers,
The four decision makers, whose weight vector is
Linguistic assessments of the five alternatives.
Decision makers | Alternatives | Criteria | |||
C_{1} | C_{2} | C_{3} | C_{4} | ||
DM_{1} | A_{1} | G | G | G | M-G |
A_{2} | G | M | M-G | G | |
A_{3} | M-G | G | M-G | ||
A_{4} | G | G | M-G | VG | |
A_{5} | G-VG | VG | G | G | |
DM_{2} | A_{1} | VG | M | MG | MG-G |
A_{2} | G | M-MG | MG | M | |
A_{3} | G | MG-G | G | ||
A_{4} | MG | MG | G | G | |
A_{5} | G-VG | G | G | VG | |
DM_{3} | A_{1} | VG | MG | MG-VG | G |
A_{2} | G | M | MG | M-MG | |
A_{3} | M-G | G | G | MG | |
A_{4} | M | M | G | ||
A_{5} | G-EG | G | G-VG | G | |
DM_{4} | A_{1} | G | M | G-VG | G |
A_{2} | M-G | M-G | G | M | |
A_{3} | G | VG | G-VG | G | |
A_{4} | G | G | G | ||
A_{5} | G-VG | VG | VG | G |
In the following, we utilize the proposed decision making approach to derive the most desirable green supplier, which consists of the following steps:
Interval 2-tuple linguistic assessment matrixes of the four decision makers.
Decision makers | Candidates | Criteria | |||
C_{1} | C_{2} | C_{3} | C_{4} | ||
DM_{1} | A_{1} | ||||
A_{2} | |||||
A_{3} | |||||
A_{4} | |||||
A_{5} | |||||
DM_{2} | A_{1} | ||||
A_{2} | |||||
A_{3} | |||||
A_{4} | |||||
A_{5} | |||||
DM_{3} | A_{1} | ||||
A_{2} | |||||
A_{3} | |||||
A_{4} | |||||
A_{5} | |||||
DM_{4} | A_{1} | ||||
A_{2} | |||||
A_{3} | |||||
A_{4} | |||||
A_{5} |
Individual overall assessment values of the alternatives.
Alternatives | Decision makers | |||
DM_{1} | DM_{2} | DM_{3} | DM_{4} | |
A_{1} | ||||
A_{2} | ||||
A_{3} | ||||
A_{4} | ||||
A_{5} |
Collective overall assessment values of the alternatives.
Alternatives | |||||
A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | |
By ITHA | |||||
By ITOWAWA | |||||
By ITHG |
The
Ranking | ||||||
ITHA | 2.799 | 0.888 | 2.753 | 1.560 | 4.500 | |
ITOWAWA | 2.656 | 0.860 | 2.613 | 1.871 | 4.500 | |
ITHG | 2.697 | 0.863 | 2.682 | 1.774 | 4.484 |
Rankingsof the five alternative suppliers.
Alternatives | |||||
A_{1} | A_{2} | A_{3} | A_{4} | A_{5} | |
ITHA | 2 | 5 | 3 | 4 | 1 |
ITOWAWA | 2 | 5 | 3 | 4 | 1 |
ITHG | 2 | 5 | 3 | 4 | 1 |
It may be mentioned that depending on the particular type of aggregation operator used in the proposed green supplier selection method, the results may be different leading to different rankings of the considered suppliers. As a result, the decision maker can select the most suitable green supplier according to their interests and the actual needs. But in this example, it seems clear that A5 is the optimal choice.
To further validate the proposed approach, we provide a comparative analysis with some existing green supplier selection methods for the above case study, which include the fuzzy TOPSIS (Fallahpour
Ranking results according to the comparative methods.
Alternatives | Fuzzy TOPSIS | COPRAS-G | ITL-VIKOR | The proposed method | |||
Ranking | Ranking | Ranking | |||||
A_{1} | 0.493 | 2 | 0.201 | 2 | 0.713 | 3 | 2 |
A_{2} | 0.123 | 5 | 0.181 | 5 | 0.988 | 5 | 5 |
A_{3} | 0.475 | 3 | 0.200 | 3 | 0.512 | 2 | 3 |
A_{4} | 0.310 | 4 | 0.190 | 4 | 0.909 | 4 | 4 |
A_{5} | 1.000 | 1 | 0.229 | 1 | 0.000 | 1 | 1 |
Rankings of suppliers by the four different methods.
From Table
Green supply chain management is a hot topic in recent years due to the increasing level of pollution and the deterioration of the environment. In this study, we examined the green supplier selection problems in which the criteria values are in the form of interval 2-tuples. First, we introduced some interval 2-tuple linguistic hybrid aggregation operators, such as the ITHA operator, the ITOWAWA operator and the ITHG operator. Furthermore, we applied the developed operators to deal with multiple criteria green supplier selection problems under the interval 2-tuple linguistic environment. Finally, a practical example in the automobile manufacturing industry has been given to verify the developed green supplier selection approach and to demonstrate its benefits and effectiveness. The results show that the proposed method is straightforward and has no loss of information; the decision makers can naturally provide their assessments by using the interval 2-tuple linguistic approach under multi-granular linguistic context.
In the future, we expect to develop further extensions to the proposed green supplier selection approach by adding new characteristics in the decision process, such as the use of dependent aggregation operators (Liu
The authors are very grateful to the editor and reviewers for their insightful and constructive comments and suggestions which are very helpful in improving the quality of the paper. This work was partially supported by the National Natural Science Foundation of China (Nos. 61773250, 71671125 and 71402090) and the Shanghai Youth Top-Notch Talent Development Program.