Fuzzy Multiple Attribute Decision Making for Evaluating Aggregate Risk in Green Manufacturing

TSINGHUA SCIENCE AND TECHNOLOGY ISSN 1007-0214 19/20 pp627-632 Volume 10, Number 5, October 2005

Fuzzy Multiple Attribute Decision Making for Evaluating Aggregate Risk in Green Manufacturing* LIU Hua (ঞ

‫)ܟ‬, CHEN Weiping (чป଼)**, KANG Zhixin (ࢢᄝ໭), NGAI Tungwai, LI Yuanyuan (ह၍၍)

College of Mechanical Engineering, South China University of Technology, Guangzhou 510640, China Abstract: Industrial risk and the diversification of risk types both increase with industrial development. Many uncertain factors and high risk are inherent in the implementation of new green manufacturing methods. Because of the shortage of successful examples and complete and certain knowledge, decision-making methods using probabilities to represent risk, which need many examples, cannot be used to evaluate risk in the implementation of green manufacturing projects. Therefore, a fuzzy multiple attribute decision-making (FMADM) method was developed with a three-level hierarchical decision-making model to evaluate the aggregate risk for green manufacturing projects. A case study shows that the hierarchical decision-making model of the aggregate risk and the FMADM method effectively reflect the characteristics of the risk in green manufacturing projects. Key words: green manufacturing; fuzzy multiple attribute decision making; aggregate risk; fuzzy logic

Introduction Environmental pollution, resource allocation, and population growth are the three main problems confronting mankind. Environmental pollution is worsening and is becoming a serious threat to the survival and development of society. Sustainable development has become the key policy by which we can control environmental pollution and resource usage while still developing. Sustainable production and consumption will be the main characteristics of future societies to provide sustainable development and a sustainable society[1,2]. The manufacturing industry is one of the main sources of environmental  γ

Received: 2004-03-01; revised: 2004-12-20 Supported by the National Natural Science Foundation of China (No. 50135020), the National High-Tech Research and Development (863) Program of China (No. 2001AA337010) and the Key Grant Project of the Ministry of Education, China (No. 0203)

γγ To whom correspondence should be addressed. E-mail: [email protected]; Tel: 86-20-87112948

pollution. Therefore, all industries are seeking to minimize the environmental impact of their industry[3]. Green manufacturing, which is an advanced manufacturing mode, is the application of sustainable science to the manufacturing industry. In the 21st century, the manufacturing industry must seek to minimize environmental impact and resource consumption during the entire product life cycle which includes design, production, processing, packaging, transport, and use of products in continuous or discrete manufacturing industries[4-6]. Industrial risk and the diversification of risk types have both increased with industrial development. At the same time, the risk acceptability threshold of the population has decreased. In response, industry has developed methodologies for risk prevention and protection[7]. Green manufacturing was first proposed about ten years ago, so there are few examples that can be used to evaluate risks and many uncertain factors. Because of this incomplete and uncertain knowledge, decision-making methods using probabilities to

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represent risk, which need many examples, cannot be used for green manufacturing projects. In addition, green manufacturing involves a very wide range of topics, such as environmental consciousness, life cycle thinking, and sustainable development, which increase the risk. Therefore, risk decision-making in green manufacturing projects must consider multiple indicators. With more than 4 indicators in a problem, the analytic hierarchical process (AHP) method cannot easily find a consistent condition for its judgment matrix[8-10], so that the AHP method is not appropriate for green manufacturing projects. Other general risk analysis methods are also not very effective. This paper uses fuzzy numbers to represent the uncertain risk information in green manufacturing projects and to integrate the available knowledge into a fuzzy multiple attribute decision-making (FMADM) method[11,12].

1

Hierarchical Structure Model of Aggregate Risk

Enterprises are implementing green manufacturing projects for sustainable production for four types of risk categories: technological, organizational, financial, and circumstancial. Each category is related to some risk factors. Analysis of typical risk factors in green manufacturing projects led to the hierarchical decisionmaking model of the aggregate risk shown in Fig. 1.

Technological risk Since the concept of green manufacturing is relatively new, its theories and technologies are still being developed. Only experience will show whether or not each technology can be used in green manufacturing projects to create extended benefits for industry, society, and the ecology. Therefore, there are many technological risk factors, including its reliability, maintenance, and applicability. Organizational risk Green manufacturing is a new manufacturing mode with the product cycle extending to the entire product life (raw materials, production, use, recycle, and disposal), so traditional management methods are not suitable. Therefore, the management system must be reformed to successfully implement green manufacturing which will lead to unpredictable risks. The main organizational risk factors are the integration of the management approach, the knowledge level of the lead group, and the knowledge level of the personnel. Financial risk Green manufacturing projects require a very long investment period due to the length of the entire product cycle which increases the risk. Corporate income is gained by saving energy and materials, protecting the environment and workers, inproving productivity and product quality, reducing costs, and accurating market timing. Circumstancial risk Green manufacturing projects are constrained not only by internal resources but also by external resources. Many uncertain circumstancial factors can cause critical risks. Such external factors include laws, regulations, macro economic changes, and industrial development.

2

Fig. 1 Hierarchical decision-making framework of aggregate risk

Fuzzy Multiple Attribute Approaches

The hierarchical decision-making framework for the aggregate risk shown in Fig. 1 was used to develop an FMADM method for risk decision of green manufacturing projects. Linguistic values were used to denote the relative importance of each attribute and each risk item and to denote the risk grade of each risk item in the project. The linguistic values were then translated into normal triangular fuzzy numbers. The fuzzy average weighted method was then used to compute the aggregate risk for each project as a triangular fuzzy number. The centroid method was then

LIU Hua ঞ

‫ ܟ‬et al˖Fuzzy Multiple Attribute Decision Making for EvaluatingĂĂ

used to convert the triangular fuzzy numbers to the real numbers representing the aggregate risk of each project. 2.1

Application of triangular fuzzy numbers

A fuzzy number is a convex fuzzy set characterized by a given interval of real numbers[13], each with a membership grade between 0 and 1. Its membership function is piecewise continuous and satisfies the following conditions: a) µA=0 for each x  (f, a1 ] ‰ [a4 , f],

b) µA is non-decreasing on [a1,a2] and non-increasing on [a3,a4], c) µA=1 for each xę[a2,a3], where a1 ” a2 ” a3 ” a4 are real numbers on the real line R. Triangular fuzzy numbers are a special class of fuzzy numbers defined by three real numbers and often expressed as (a, b, c). Their membership functions are usually described as ­( x  a ) (b  a ), a d x d b; ° P A ®(b  x) /(c  b), b d x d c; (1) °0, otherwise ¯ where b is the most possible value of the fuzzy number A, and a and c are the lower and upper bounds which are often used to illustrate the fuzziness of the data. Let A1=(a1, b1, c1) and A2=(a2, b2, c2) be two positive triangular fuzzy numbers. The basic fuzzy arithmetic operations on these fuzzy numbers are defined as: a) Inverse: A–1=(1/c, 1/b, 1/a). b) Addition: A1+A2=(a1+a2, b1+b2, c1+c2). c) Subtraction: A1–A2=(a1– c2, b1–b2, c1–a2). d) Scalar multiplication )k > 0, kęR, kA=(ka, kb, kc); ) k < 0, kęR, kA=( kc, kb, ka). (e) Multiplication: A1A2=(a1a2, b1b2, c1c2). (f) Division: A1/A2=(a1/c2, b1/b2, c1/a2). Fuzzy numbers are intuitively easy to use in expressing the decision maker’s qualitative assessments[14]. A linguistic variable is a variable whose values are not numbers but words or phrases in a natural or synthetic language. Linguistic variables are used to denote the relative importance of each attribute and of each risk item, as well as the risk grade of each risk item in a project. The linguistic value set is {Definitely low, Extra low, Very low, Low, Slightly

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low, Middle, Slightly high, High, Very high, Extra high, Definitely high}. The set is represented by a normal triangular fuzzy number as shown in Table 1 and Fig. 2. Table 1 Normal triangular fuzzy numbers for linguistic values, grade of risk, and grade of importance Linguistic value Normal fuzzy number

Grade Grade of of risk importance 1 1

Definitely low

N1˙(0.0, 0.0, 0.1)

Extra low

N2˙(0.0, 0.1, 0.2)

2

2

Very low

N3˙(0.1, 0.2, 0.3)

3

3

Low

N4˙(0.2, 0.3, 0.4)

4

4

Slightly low

N5˙(0.3, 0.4, 0.5)

5

5

Middle

N6˙(0.4, 0.5, 0.6)

6

6

Slightly high

N7˙(0.5, 0.6, 0.7)

7

7

High

N8˙(0.6, 0.7, 0.8)

8

8

Very high

N9˙(0.7, 0.8, 0.9)

9

9

Extra high

N10˙(0.8, 0.9, 1.0)

10

10

Definitely high

N11˙(0.9, 1.0, 1.0)

11

11

Fig. 2 Linguistic value membership functions

2.2

Weight calculating method

The importance of each attribute in the attribute set in Fig. 1 is first given a value from the linguistic value set which is then translated into a relevant normal triangular fuzzy number. Then, the importance of each risk item is defined relative to the attribute in the same way. Finally, the normal triangular fuzzy number representing the importance of each risk item and its attribute are combined into the weight of each risk item. Let n(i) be the number of risk items for attribute Ri. In Fig. 1, n(1)˙4, n(2)˙3, n(3)˙3, and n(4)˙2. Let W(i) denote the relative weight given to attribute Ri as a normal triangular fuzzy number in [0, 1]. Let W(i,,j) denote the relative weight given to each risk item Ri,j (i ˙ 1, 2, 3, 4, j ˙ 1,2,…,n(i)) as a normal triangular fuzzy number in [0, 1]. Then let Wi,j denote the weight

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given to risk item Ri,j. Then Wi,j can be expressed as (2) Wi,j˙W(i) W(i,,j) where W(i)˙(a(i), b(i), c(i)), W(i,j)˙(a(i,j), b(i,j), c(i,j)), and Wi,j˙(a(i)a(i,j), b(i)b(i,j), c(i)c(i,j)). 2.3

zm

Table 2 Attribute

R1

R2

4 n (i )

¦¦W

i, j

X i , j ,m

R3

i 1 j 1

Zm

4 n(i )

¦¦W

R4

i, j

i 1 j 1

(4)

where zm represents the aggregate risk of project Pm as a real number.

Fuzzy average weighting method

The symbol Xi,j,m is used to denote the risk grade of risk item Ri,j of project Pm (m=1,2,…,k, where k is the number of projects to be evaluated) as a normal triangular fuzzy number translated from the linguistic value. Table 2 represents the relative signs between the various variables used for the risk assessment. The final aggregate risk is calculated using the fuzzy average weighting method defined by:

am  bm  cm 3

Risk item R1,1 R1,2 R1,3 R1,4 R2,1 R2,2 R2,3 R3,1 R3,2 R3,3 R4,1 R4,2

Model structure for project Pm Attribute importance

W(1)

W(2)

W(3)

W(4)

Risk item importance W(1,1) W(1,2) W(1,3) W(1,4) W(2,1) W(2,2) W(2,3) W(3,1) W(3,2) W(3,3) W(4,1) W(4,2)

Weight W1,1 W1,2 W1,3 W1,4 W2,1 W2,2 W2,3 W3,1 W3,2 W3,3 W4,1 W4,2

Risk grade X1,1,m X1,2,m X1,3,m X1,4,m X2,1,m X2,2,m X2,3,m X3,1,m X3,2,m X3,3,m X4,1,m X4,2,m

4 n(i )

¦¦W

W( i , j ) X i , j , m

3

(i )

i 1 j 1

(am , bm , cm )

4 n (i )

¦¦W

W(i , j )

(i )

i 1 j 1

where Zm is a triangular fuzzy number which represents the aggregate risk of project Pm. 4 n (i )

¦¦ a

4 n(i )

a

i, j i, j ,m

am

i 1 j 1

¦¦ ci , j i 1 j 1

4 n (i )

bm

b

¦¦ bi , j i 1 j 1

4 n(i )

cm

,

4 n(i )

¦¦ c(i ) c(i, j ) i 1 j 1

¦¦ b

b

b

(i ) (i , j ) i , j , m i 1 j 1 4 n (i )

,

¦¦ b(i )b(i , j ) i 1 j 1

4 n(i )

c

i, j i, j ,m i 1 j 1 4 n (i )

¦¦ ai, j i 1 j 1

a

4 n(i )

i, j i, j ,m i 1 j 1 4 n(i )

¦¦ c

a

(i ) (i, j ) i, j ,m

i 1 j 1

4 n(i )

¦¦ b

¦¦ a

¦¦ c

c

c

(i ) (i, j ) i , j ,m i 1 j 1 4 n (i )

Case Study

(3)

.

¦¦ a(i ) a(i, j ) i 1 j 1

These triangular fuzzy numbers for all the projects are then translated to real numbers representing the aggregate risk for each project. These real numbers are then used to rank the aggregate risk of each project. The centroid method is the most popular method for ranking triangular fuzzy numbers. With the centroid method, the triangular fuzzy number is converted to a real number as

The case involves a refrigerator company that makes a strategic plan to implement ISO14000 series standards to achieve sustainable green manufacturing production. The standards are divided into three phases: ISO14001 certification, life cycle assessment, and environmental labeling. For the ISO14001 certification phase, decision-makers analyze three scenarios for implementing ISO14001 certification. The first project obtains ISO9001 certification and then ISO14001 certification. The second project obtains ISO9001 certification and ISO14001 certification at the same time. The third project obtains ISO14001 certification and then ISO9001 certification. The FMADM method was then used to evaluate the aggregate risk in implementing each of these three scenarios. The calculational procedure was as follows: Step 1 Hierarchical decision-making framework for aggregate risk is set up, as shown in Fig. 1. Step 2 Calculate risk item weights. The grades of importance in Table 1 are used to assign the relative weights of the risk attributes and the risk items in Fig. 1 which are then translated into fuzzy numbers. The risk item weights are then calculated using Eq. (2). Step 3 Calculate the aggregate risk for every scenario.

LIU Hua ঞ

‫ ܟ‬et al˖Fuzzy Multiple Attribute Decision Making for EvaluatingĂĂ

The risk grades in Table 1 are used to calculate the risk grades of all risk items in each project which are then translated into fuzzy numbers. The aggregate risk of every project is then calculated by Eq. (3). Step 4 Rank projects. The fuzzy numbers which represent the aggregate risk of each project are then translated back into real numbers using Eq. (4). These real numbers are then used to rank each scenario’s aggregate risk. Table 3 Attribute

R1

Weights and grades of risk for the three scenarios Weight (Wi,j)

R1,1

(0.0,0.0,0.1))

(0.00,0.00,0.05)

R1,2

(0.2,0.3,0.4)

(0.06,0.12,0.20)

(0.0,0.1,0.2)

(0.00,0.04,0.10)

R1,4

(0.1,0.2,0.3)

(0.03,0.08,0.15)

R2,1

(0.0,0.0,0.1)

(0.00,0.00,0.03)

(0.1,0.2,0.3)

(0.01,0.04,0.09)

R2,3

(0.4,0.5,0.6)

(0.04,0.10,0.18)

R3,1

(0.0,0.1,0.2)

(0.00,0.01,0.04)

R1,3

Attribute importance (W(i))

(0.3,0.4,0.5)

R2,2 R2

(0.1,0.2,0.3)

R3,2

(0.1,0.2,0.3)

(0.00,0.02,0.06)

R3,3

(0.5,0.6,0.7)

(0.00,0.06,0.14)

R4,1

(0.6,0.7,0.8)

(0.00,0.07,0.16)

(0.1,0.2,0.3)

(0.00,0.02,0.06)

R3

R4

The decision-making data is listed in Table 3. The results given in Table 4 show that scenario P3 has the highest aggregate risk, while scenario P1 has the lowest aggregate risk. Therefore, the company implemented scenario P1, which resulted in great improvements in their technology and management as well as remarkable economic benefits. The case study results show the effectiveness of the risk decision-making method presented in this paper.

Risk item importance (W(i,j))

Risk item

(0.0,0.1,0.2)

R4,2

631

(0.0,0.1,0.2)

Risk grade (Xi,j,m) (P1)(0.5,0.6,0.7) (P2)(0.6,0.7,0.8) (P3)(0.2,0.3,0.4) (P1)(0.1,0.2,0.3) (P2)(0.4,0.5,0.6) (P3)(0.6,0.7,0.8) (P1)(0.6,0.7,0.8) (P2)(0.4,0.5,0.6) (P3)(0.5,0.6,0.7) (P1)(0.2,0.3,0.4) (P2)(0.5,0.6,0.7) (P3)(0.6,0.7,0.8) (P1)(0.2,0.3,0.4) (P2)(0.2,0.3,0.4) (P3)(0.2,0.3,0.4) (P1)(0.4,0.5,0.6) (P2)(0.5,0.6,0.7) (P3)(0.4,0.5,0.6) (P1)(0.3,0.4,0.5) (P2)(0.7,0.8,0.9) (P3)(0.8,0.9,1.0) (P1)(0.5,0.6,0.7) (P2)(0.4,0.5,0.6) (P3)(0.6,0.7,0.8) (P1)(0.2,0.3,0.4) (P2)(0.1,0.2,0.3) (P3)(0.5,0.6,0.7) (P1)(0.4,0.5,0.6) (P2)(0.0,0.1,0.2) (P3)(0.1,0.2,0.3) (P1)(0.0,0.1,0.2) (P2)(0.0,0.0,0.1) (P3)(0.0,0.0,0.1) (P1)(0.6,0.7,0.8) (P2)(0.4,0.5,0.6) (P3)(0.0,0.1,0.2)

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Table 4

Project results

[5] Yang Shuzi, Wu Bo. Trends in the development of

Pm (Project)

Zm

zm

Rank

P1

(0.022,0.355,4.336)

1.571

3

P2

(0.057,0.459,4.886)

1.801

2

P3

(0.071,0.548,5.429)

2.016

1

advanced manufacturing technology. Chinese Journal of Mechanical

Engineering,

2003,

39(10):

73-78.

(in

Chinese) [6] Wang Xiankui. Broad manufacturing theory. Chinese Journal of Mechanical Engineering, 2003, 39(10): 87-94.

4

Conclusions

A hierarchical decision-making framework was developed to evaluate the aggregate risk in green manufacturing projects. Linguistic variables and fuzzy numbers were used to represent the uncertain or fuzzy information. Fuzzy arithmetic operations were used to combine the data. The FMADM method is especially suitable for decision-making with incomplete information and multiple indicators, which are common problems in green manufacturing decision making. The method can be easily implemented in software as a model for other risk analysis software.

( in Chinese) [7] Tixer J, Dusserre G, Salvi O, et al. Review of 62 risk analysis methodologies of industrial plants. Journal of Loss Prevention in the Process Industries, 2002, 15: 291-303. [8] Leung L C, Cao D. On consistency and ranking of alternatives

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Operational Research, 2000, 124: 102-113. [9] Sadig R, Radriguez M J. Fuzzy synthetic evaluation of disinfection by-productsüA risk-based indexing system. Journal of Environmental Management, 2004, 73: 1-13. [10] Chan F T J, Jiang B, Tang N K H. The development of intelligent decision support tools to aid the design of flexible manufacturing systems. International Journal of Production Economics, 2000, 65: 73-84.

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