Research on supply chain risk assessment with intuitionistic fuzzy information

Abstract

The paper suggests an intuitionistic fuzzy operator to assess supply chain risk. With the global economic integration trend, more and more enterprises adopt the modern management model of supply chain in order to have access to the advantage of responding quickly to the market demand. Through the implementation of supply chain management, their management efficiency has been significantly improved which led to brought good economic benefits. However, at the same time risk is becoming an unavoidable problem for the enterprises in supply chain, because of the uncertainty of the environment of the supply chain and the ever-increasing complexity of its own. The management of supply chain risk assessment has attracted increasing attention of theoretical and business research. The study investigates the supply chain risk assessment with intuitionistic fuzzy information, and then proposes a dependent intuitionistic fuzzy Hamacher weighted geometric (DIFHWG) operator. This operator is used to design an algorithm for supply chain risk assessment with intuitionistic fuzzy numbers. To demonstrate the effectiveness of this approach, several experiments are conducted to verify the developed method.

Keywords

Intuitionistic fuzzy information operational laws dependent intuitionistic fuzzy Hamacher weighted geometric (DIFHWG) operator supply chain risk assessment

1 Introduction

Many abilities of project are the key successful factors under the new economic environment, such as quick response ability, resource optimum combination ability, learning ability, forward-looking exploration ability and so on. But the traditional problems of project management (ex, quality accident, duration dragging, expense overspending, and engineering claim) are still very serious, and the primary cause is project participants share an oppositional and short-term relationship to each other which results by one-off custom-made production mode cored by project. Consequently, project integration management emerges as the times require under the supply chain circumstance. With the rapid development of science and technology and the increasing global competition, market competition has been becoming competition between supply chains from that of enterprises. As the important strategic sources of firms, knowledge has been a critical factor for firms of supply chain to obtain competitive advantage and sustainable competitive power. The overall operational efficiency and competitive power of supply chain can be improved through transferring and sharing intellectual resources in supply chain. However, knowledge transfer makes the firms face knowledge transfer risks. Therefore, it is meaningful to the improvement of supply chain operation efficiency and to the further development of supply chain members to exploring the knowledge transfer risk in supply chain. Unfortunately, in the practice, knowledge transfer risk management in supply chain has not raised sufficient attention of peoples. Supply chain members ignore the existence of knowledge transfer risks while they are concerning to knowledge transfer advantages, and the results is that the members bear many unnecessary loss in the process of knowledge transferring. In theoretical circles, the researches on knowledge management of supply chain mainly focus on knowledge sharing and transfer, knowledge learning and knowledge absorption, and the realization of knowledge transferring. Though there are some related literatures which explore the knowledge transfer risks, most of them are prevention methods and countermeasures on a single risk or some risks, system of theory and method of knowledge transfer risk management of supply chain has not formed yet. However, under the circumstance of supply chain management (SCM), some tendencies exposed enterprises to increasing logistics risk. The tendencies include: more complicate of logistics system, leaner of the supply chain, more complicate of the environment and fiercer of the competition. Therefore, it becomes urgent for enterprises to implement the logistics risk management, the focus of which is early warning. Furthermore, the key point of early warning management is the early warning indicator system (EWIS) of enterprise logistics. So it is necessary for enterprises to establish a reasonable and comprehensive EWIS of enterprise logistics. The research on EWIS is again very scarce in logistics area. Moreover, the questionnaire results that are calculated also show that although enterprises’ awareness of logistics risk is rather lack, their desire for the effective, specialized and systematic knowledge on enterprise logistics risk management is strong. The integrated nature of logistics processes necessitates that logistics risk be assessed from the SCM’s perspective rather than the single company’s perspective. Therefore, the research on the EWIS of enterprise logistics risk based on the SCM is of great theoretical and practical significance.

The problem of supply chain risk assessment with intuitionistic fuzzy information is the multiple attribute decision making problems [1 –14]. This paper studies on the supply chain risk assessment with intuitionistic fuzzy information. The study proposes the dependent intuitionistic fuzzy Hamacher weighted geometric (DIFHWG) operator. In the end, this paper provides an example to make performance evaluation.

2 Preliminaries

Some definitions are given as follows.

Definition 1. [15, 16] An IFS A in X is given by $A = {〈 x, μ_{A} (x), ν_{A} (x) 〉 | x \in X}$ (1)

where μ_A : X → [0, 1] and ν_A : X → [0, 1], with the condition 0 ≤ μ_A (x) + ν_A (x) ≤ 1, ∀ x ∈ X.

Definition 2. [17] Let $\tilde{a} = (μ, ν)$ be an intuitionistic fuzzy number, a score function S can be represented as follows: $S (\tilde{a}) = μ - ν, S (\tilde{a}) \in [- 1, 1] .$ (2)

Definition 3. [18] Assume that $\tilde{a} = (μ, ν)$ is an intuitionistic fuzzy number, accuracy function H is represented as follows: $H (\tilde{a}) = μ + ν, H (\tilde{a}) \in [0, 1] .$ (3)

Xu [19] give an order relation between 2 intuitionistic fuzzy values.

Definition 4. Assume that ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ be 2 intuitionistic fuzzy values, $s ({\tilde{a}}_{1}) = μ_{1} - ν_{1}$ and $s ({\tilde{a}}_{2}) = μ_{2} - ν_{2}$ be the scores of $\tilde{a}$ and $\tilde{b}$ , and let $H ({\tilde{a}}_{1}) = μ_{1} + ν_{1}$ and $H ({\tilde{a}}_{2}) = μ_{2} + ν_{2}$ be the degrees of symbol $\tilde{a}$ and, when $S (\tilde{a}) < S (\tilde{b})$ , then $\tilde{a}$ is lower than $\tilde{b}$ , represented as $\tilde{a} < \tilde{b}$ ; if $S (\tilde{a}) = S (\tilde{b})$ , then

(1) if $H (\tilde{a}) = H (\tilde{b})$ , then $\tilde{a}$ and $\tilde{b}$ represent the same information, denoted by $\tilde{a} = \tilde{b}$ ; (2) if $H (\tilde{a}) < H (\tilde{b})$ , $\tilde{a}$ is smaller than $\tilde{b}$ , denoted by $\tilde{a} < \tilde{b}$ .

Next, the Hamacher operation on intuitionistic fuzzy sets [20] is discussed. Let the t-norm T and t-conorm S be Hamacher product T” and Hamacher sum S”, and the generalised intersection and union on two IFSs A and B mean Hamacher product (represented as ${\tilde{a}}_{1} \otimes {\tilde{a}}_{2}$ ) and Hamacher sum (denoted by ${\tilde{a}}_{1} \oplus {\tilde{a}}_{2}$ ) on two IFSs ${\tilde{a}}_{1}$ and ${\tilde{a}}_{2}$ , respectively, as follows. $\begin{matrix} {\tilde{a}}_{1} \oplus {\tilde{a}}_{2} = (\frac{μ_{1} + μ_{2} - μ_{1} μ_{2} - (1 - γ) μ_{1} μ_{2}}{1 - (1 - γ) μ_{1} μ_{2}}, \\ \frac{ν_{1} ν_{2}}{γ + (1 - γ) (ν_{1} + ν_{2} - ν_{1} ν_{2})}) \\ λ {\tilde{a}}_{1} = (\frac{{(1 + (γ - 1) μ_{1})}^{λ} - {(1 - μ_{1})}^{λ}}{{(1 + (γ - 1) μ_{1})}^{λ} + (γ - 1) {(1 - μ_{1})}^{λ}}, \\ \frac{γ {(ν_{1})}^{λ}}{{(1 + (γ - 1) (1 - ν_{1}))}^{λ} + (γ - 1) {(ν_{1})}^{λ}}) λ > 0 . \end{matrix}$

3 Dependent intuitionistic fuzzy Hamacher weighted geometric (DIFHWG) operator

Definition 5. [21] Suppose that ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ be several Intuitionistic fuzzy numbers, then their aggregated value by using the IFHWG operator is belonged to IFN as well, and $\begin{matrix} {IFHWG}_{ω} ({\tilde{a}}_{1}, {\tilde{a}}_{2}, \dots, {\tilde{a}}_{n}) = \otimes_{j = 1}^{n} {({\tilde{a}}_{j})}^{ω_{j}} \\ = (\frac{γ \prod_{j = 1}^{n} μ_{j}^{ω_{j}}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - μ_{j}))}^{ω_{j}} + (γ - 1) \prod_{j = 1}^{n} μ_{j}^{ω_{j}}}, \\ \frac{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{j})}^{ω_{j}} - \prod_{j = 1}^{n} {(1 - ν_{j})}^{ω_{j}}}{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{j})}^{ω_{j}} + (γ - 1) \prod_{j = 1}^{n} {(1 - ν_{j})}^{ω_{j}}}) \end{matrix}$ (4)

where ω = (ω₁, ω₂, …, ω_n) ^T be the weight vector of ${\tilde{a}}_{j} (j = 1, 2, \dots, n)$ , and ω_j > 0, $\sum_{j = 1}^{n} ω_{j} = 1$ .

Definition 6. [22] Assume the ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ denotes a group of intuitionistic fuzzy numbers, the average value of the of ${\tilde{a}}_{j} (j = 1, 2, \dots, n)$ is computed as $\tilde{a} = \frac{1}{n} \otimes_{j = 1}^{n} ({\tilde{a}}_{j})$ (5)

Definition 7. [23] Assume that ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ denote 2 intuitionistic fuzzy numbers,

afterwards, and the Hamming distance between ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ is defined in Equation 6. $d ({\tilde{a}}_{1}, {\tilde{a}}_{2}) = \frac{| μ_{1} - μ_{2} | + | ν_{1} - ν_{2} |}{2}$ (6)

Definition 8. [24] Let ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ be a group of intuitionistic fuzzy numbers, then call

$\begin{matrix} sim ({\tilde{a}}_{j}, \tilde{a}) & = & 1 - \frac{d ({\tilde{a}}_{j}, \tilde{a})}{\sum_{j = 1}^{n} d ({\tilde{a}}_{j}, \tilde{a})}, \\ j = 1, 2, \dots, n . \end{matrix}$ (7) the degree of similarity between the intuitionistic fuzzy values ${\tilde{a}}_{j}$ and the mean $\tilde{a}$ .

Some individuals can be assigned to repugnant objects. Hence, we allocate smaller weights to the above opinions, and the IFHWG operator weights can be computed as follows. $w_{j} = \frac{sim ({\tilde{a}}_{j}, \tilde{a})}{\sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})}, j = 1, 2, \dots, n$ (8)

Obviously, w_j ≥ 0, j = 1, 2, …, n and $\sum_{j = 1}^{n} w_{j} = 1$ .

Particularly, if ${\tilde{a}}_{j} = \tilde{a}$ is satisfied, for all i, j = 1, 2, …, n, then by (8), we have $w_{j} = \frac{1}{n}$ , for all j = 1, 2, …, n.

By (4), we have

$\begin{matrix} IFHWG ({\tilde{a}}_{1}, {\tilde{a}}_{2}, \dots, {\tilde{a}}_{n}) = \otimes_{j = 1}^{n} {({\tilde{a}}_{j})}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})} \\ = (\frac{γ \prod_{j = 1}^{n} μ_{j}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - μ_{j}))}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})} + (γ - 1) \prod_{j = 1}^{n} μ_{j}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})}}, \\ \frac{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{j})}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})} - \prod_{j = 1}^{n} {(1 - ν_{j})}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})}}{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{j})}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})} + (γ - 1) \prod_{j = 1}^{n} {(1 - ν_{j})}^{sim ({\tilde{a}}_{j}, \tilde{a}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{j}, \tilde{a})}}) \end{matrix}$ (9)

We use Equation 9 a dependent intuitionistic fuzzy Hamacher weighted geometric (DIFHWG) operator.

4 Research on supply chain risk assessment with intuitionistic fuzzy information

We use DIFHWG operator for supply chain risk assessment problems with intuitionistic fuzzy numbers. Let A ={ A₁, A₂, …, A_m } be a discrete set of alternatives, and G ={ G₁, G₂, …, G_n } is a set of attributes. Suppose that $\tilde{R} = {({\tilde{r}}_{ij})}_{n \times m} = {(μ_{ij}, ν_{ij})}_{n \times m}$ is the intuitionistic fuzzy evaluation matrix, μ_ij ⊂ [0, 1], ν_ij ⊂ [0, 1], μ_ij + ν_ij ≤ 1, i = 1, 2, …, m, j = 1, 2, …, n,

Next, the DIFHWG operator is used for supply chain risk assessment problem with intuitionistic fuzzy information. The method is made up of the following steps:

Step 1. Use the evaluation information given in matrix $\tilde{R}$ , and the DIFHWG operator

$\begin{matrix} {\tilde{r}}_{i} = (μ_{i}, ν_{i}) = DIFHWG ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in}) = \otimes_{j = 1}^{n} {({\tilde{a}}_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})} \\ = (\frac{γ \prod_{j = 1}^{n} {(μ_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - μ_{ij}))}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})} + (γ - 1) \prod_{j = 1}^{n} μ_{ij}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})}}, \\ \frac{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})} - \prod_{j = 1}^{n} {(1 - ν_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})}}{\prod_{j = 1}^{n} {(1 + (γ - 1) ν_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})} + (γ - 1) \prod_{j = 1}^{n} {(1 - ν_{ij})}^{sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i}) / \sum_{j = 1}^{n} sim ({\tilde{a}}_{ij}, {\tilde{a}}_{i})}}) \end{matrix}$

Step 2. Compute the scores $S ({\tilde{r}}_{i}) (i = 1, 2, \dots, m)$ of the collective overall values ${\tilde{r}}_{i} (i = 1, 2, \dots, m)$ to rank all the alternatives A_i (i = 1, 2, …, m) to choose the best one(s).

Step 3. Rank all the alternatives A_i (i = 1, 2, …, m) and choose the optimal one according to $S ({\tilde{r}}_{i})$ and $H ({\tilde{r}}_{i}) (i = 1, 2, \dots, m)$ .

Step 4. End.

5 Numerical example

Supply chain has been evolved into a complex network where some connected agents, including supplier, manufacturer, distributor and retailer and so on, work together to transform raw material into finished goods and meet the demand of market. Since there is a close relationship among agents, disruption which one agent is subject to can accumulate, amplify, mutant, and propagate along the supply chain network. As a result, the disruption risk may evolve into a serious crisis. This kind of phenomenon caused by some serious events has seriously affecting supply chain and compels people to pay

enough attention to its cause. Recently the relationship between domestic enterprises and oversea ones has been closer. Apparently, one enterprise not only can benefit from supply chain management, but also improve the relevance of risks between it and other enterprise in the practice of supply chain management. The relevance has an important effect on supply chain network because it may become one pathway or mechanism which disruption risks occurred in one agent propagate throughout the supply chain network. How to avoid and control disruption risk propagation has been an issue for Chinese enterprise, and it is critical to study and reveal the mechanism of disruption risk propagation in supply chain. The problems of supply chain risk assessment problems with intuitionistic fuzzy information are the multiple attribute decision making problems. This section presents a numerical example for supply chain risk assessment with intuitionistic fuzzy information to describe this approach. There are five possible logistics enterprises A_i (i = 1, 2, 3, 4, 5) for four attributes G_j (j = 1, 2, 3, 4). The four attributes include the ①G₁ is the time of delivery risk; ②G₂ is the delivery quantity risk; ③G₃ is the delivery quality risk; ④G₄ is the delivery price risk. The five possible logistics enterprises A_i (i = 1, 2, 3, 4, 5) are to be evaluated under the given 4 attributes as follows in Table 1.

Next, the DIFHWG operator is utilized for supply chain risk assessment with intuitionistic fuzzy information.

Step 1. If we apply the DIFHWG operator to decision making with intuitionistic fuzzy information, we get the weight of DIFHWG operator is: $w = (0.22, 0 . 34, 0 . 23, 0 . 21) .$

Step 2. Utilize the evaluation information given in matrix $\tilde{R}$ , and the DIFHWG operator, we get the values ${\tilde{r}}_{i}$ of the logistics enterprises A_i (i = 1, 2, …, 5). $\begin{matrix} {\tilde{r}}_{1} & = & (0.54, 0.28), {\tilde{r}}_{2} = (0.45, 0.37) \\ {\tilde{r}}_{3} & = & (0.68, 0.17), {\tilde{r}}_{4} = (0.44, 0.32) \\ {\tilde{r}}_{5} & = & (0.45, 0.28) \end{matrix}$

Step 3. Compute the scores $S ({\tilde{r}}_{i}) (i = 1, 2, \dots, 5)$ of the intuitionistic fuzzy information ${\tilde{r}}_{i} (i = 1, 2, \dots, 5)$ $\begin{matrix} S ({\tilde{r}}_{1}) & = & 0.26, S ({\tilde{r}}_{2}) = 0.08, S ({\tilde{r}}_{3}) = 0.51 \\ S ({\tilde{r}}_{4}) & = & 0.12, S ({\tilde{r}}_{5}) = 0.17 \end{matrix}$

Step 4. Rank all the logistics enterprises A_i (i = 1, 2, 3, 4, 5) according to the scores $S ({\tilde{r}}_{i})$ of the values ${\tilde{r}}_{i} (i = 1, 2, \dots, 5)$ : A₃ ≻ A₁ ≻ A₅ ≻ A₄ ≻ A₂, and then the optimal one is A₂.

6 Conclusion

The risk management of supply chain has received the emphasis from theory horizon and business community. And many supply chain risk issues have indicated that it would cause irreversible loss and even thoroughly destroy to supply chain once some kinds of risk really happened, hence design and optimization of supply chain without considering its risk is deficient. In addition, logistics system is the bottleneck of supply chain and one of the most critical factors that hard to be realized, hence to a great extent, the effects of the optimization of supply chain can be totally examined through evaluating its logistics system. Consequently, extending research of evaluating on optimization model and relevant issues of supply chain is possessed of more than some theory meanings, but some guidance values to practice work. The study investigates the supply chain risk assessment with intuitionistic fuzzy information. To testify the effectiveness of this algorithm, several experiments are conducted to make performance evaluation.

Footnotes

Acknowledgments

The paper is supported the Aviation Science Foundation of China (Grant No.2014ZG51075) and the Technical Research Foundation. The study is also sponsored by the National Natural Science Foundation of China (Grant No. 71501007).

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