Page 89 - مجله مدیریت سبز - شماره 2 - نسخه فلش

353
Non-fuzzy weights for different life-cycle phases.
Normalised weights
Non-fuzzy weights
0.520
0.493
W 1
0.290
0.275
W 2
0.057
0.060
W 3
0.138
0.131
W 4
0.043
0.046
W 5
Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
Table 6
proposed by Buckley (1985):
Step 2.
Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
Comparative weightings of life-cycle phases and its associated criteria.
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
Local weights
Life-cycle phase
Integrated weights
2
?
1
(3)
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
ij
ij
proposed by Buckley (1985):
Uw i
Lw i
Mw i
Mw i
Lw i
0.715
0.493
0.503
0.341
? is the index referring to different experts with a total of E experts.
The superscript in Equation (3)
L 1
? 1=E
2
E
1
0.158
0.046
0.019
0.092
~ a ij ¼ ~ a 5~ a 5…5~ a
0.056
0.046
0.113
LC 11
ij
ij
ij
Step 3.
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
0.471
0.337
0.138
0.137
0.159
0.054
0.274
LC 12
0.062
0.125
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
0.021
0.051
0.098
0.174
0.049
LC 13
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
0.016
0.123
0.020
0.036
0.046
0.088
0.072
LC 14
1=n
(4)
0.233
0.522
0.096
0.124
0.729
0.281
0.464
Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
~ r i ¼?~ a i1 5~ a i2 5…5~ a in
LC 15
Step 3. ?
0.424
0.175
0.272
0.275
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
L 2
?1
0.056
0.081
0.023
0.131
0.009
0.022
0.053
(5)
LC 21
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
0.018
0.045
0.107
1=n
0.018
0.008
0.046
0.065
(4)
LC 22
proposed by Buckley (1985):
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
0.039
0.098
0.232
0.138
0.016
0.093
0.037
LC 23
?1 variables, the next step is to defuzzify the weights to form meaningful
Step 4. Since the calculation so far involves linguistic
0.435
0.025
0.143
0.252
0.184
0.070
0.069
? 1=E
(5)
LC 24 Table 5 H.K. Chan et al. / The British Accounting Review 46 (2014) 344e360 Uw i Non-fuzzy weights Step 2. ~ a ij ¼ ~ a 5~ a 5…5~ a E ij ? 1=E Use the synthetic pairwise comparison matrix from Step 2. ~ a ij ¼ ~ a 5~ a 5…5~ a far the most (3)
?
E
1
2
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
ij
LC 25 0.277 0.463 0.732 0.048 0.126 0.310 0.125 ?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area ij (COA) is by ij (3)
L 3 0.039 0.056 0.087 0.057 popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each criterion (w i ) can be expressed in the
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
LC 31 0.108 0.179 0.269 0.004 0.010 0.023 0.010 following form: Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
LC 32 0.145 0.198 0.346 0.006 0.011 0.030 0.012 ?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
(6)
popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each criterion (w i ) can be expressed in the
LC 33 0.387 0.623 0.950 0.015 0.035 0.082 0.080 ~ w i ¼?Lw i ; Mw i ; Uw i ? Step 3. Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
L 4 0.083 0.128 0.204 0.131 following form: Step 2. Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
LC 41 0.549 0.789 1.097 0.046 0.101 0.224 0.102 Step 2. where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
1=n comparison matrix. This step is unnecessary if there is only one expert in Step
Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions
different experts to form one synthetic pairwise of
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
~ w i ¼?Lw i ; Mw i ; Uw i ? ) is given as:
LC 42 0.158 0.211 0.317 0.013 0.027 0.065 0.029 different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step (6) (4)
defuzzi?ed) weight value of the i-th criterion (w i
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
L 5 0.031 0.042 0.064 0.043 يارب نيون ياــهراکهار ?1
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
(
w i ¼ ½?Uw i ? Lw i ???Mw
هب يبايت??س د يارب )4( ?ل داعم زا .ت??سا ،تايح ?خرچ ياهزاف مامت زا ) ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
LC 51 0.111 0.182 0.318 0.003 0.008 0.020 0.008 يــناخرچزاب و تــيري دم يبايزرا ياه هصخشم يجوز ???سياقم زا ه دافتسا اب يطيحم تسيز ک??سير i ? Lw i ??=3 ? Lw i proposed by Buckley (1985): (7) (5)
where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
proposed by Buckley (1985):
LC 52 0.359 0.606 0.964 0.011 0.026 0.061 0.026 يتعنص ياه دحاو ر د بآ يملاک ياه سايقم . دوش يم داجيا ،يثلثم يزاف دا دعا زا ه دافتسا اب و فلتخم :اب تسا ربارب هک دينک ه دافتسا هطوبرم ياه هورگ داعبا يزاف ياه نزو E ? 1=E
defuzzi?ed) weight value of the i-th criterion (w i ) is given as:
?
2
1
~ a ij ¼ ~ a 5~ a 5…5~ a to the ?ve environmental
LC 53 0.133 0.212 0.375 0.004 0.009 0.024 0.010 Step ? 5. The next step is to calculate the environment risk ratings of different criteria with respect ij (3)
ij
ij
? 1=E
1
E
2
witteveenandbos.com . دنا ه دش فيصوت 7 لو دج ر د يطيحم تسيز يبايزرا يارب ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i 1 Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
1
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15 ? 5 ~ 5~ a 15 ? 5key difference is simply the object of the pairwise
(3)
~ a ij ¼ ~ a 5~ a 5…5~ a The procedure is similar to Step 1 to Step 4
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15 ? 5 and the
assessment attributes.
(7)
1
ij
ij
ij
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5a 14
w i
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
1=5 for different experts. A synthetic pairwise comparison
comparison. A similar matrix as in
¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? ? 2:45 ? 7:35 ? 5:48 ? 7:94? Equation (3) is the index referring to different experts with a total of E experts.
?
يجوز ?سياقم سيرتام ،يسانشراک ياه يبايزرا مامت زا ه دافتسا اب ًا د دجم 1 Equation (2) should be constructed ; ?1 1=5 The superscript in 1=5 ?1 ? 3:46 1=5 1=5 ? 1=5 ? ?
1
?
popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each criterion (w i ) can be expressed in the
?
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15 ? 5
¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93?
; ?1 ? 2:45 ? 7:35 ? 5:48 ? 7:94? ? 7:94 ? 6:48 ? 8:49?
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15 ? 5
26413997 :نارهترتف د matrix can then ? be calculated The next step is to calculate the environment risk 1=5 ; ?1 ? 2:45 the fuzzy geometric mean 1=5 1=5
?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49?
? ¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? ratings of different criteria with respect to the ?ve environmental
Step 5.using the geometric mean method outlined in Step 2. Thereafter,
? ? 7:35 ? 5:48 ? 7:94? and
The superscript in Equation (3) is the index
The environmental risk ratings of different criteria with respect to the ?ve environmental assessment attributes are نآ جياتن و ه دش هبساحم يبايزرا ياه صخاش اب طابترا ر د اهرايعم زا يبيکرت 1=5 referring to different experts with a total of E experts. 1=5 ?1 ? ? 3:46 ? 7:94 ? 6:48 ? 8:49?
1=5
1=5
1=5 1=5
Use the synthetic
following form: ?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
; ?1 ? 2:45 ? 7:35
; ?1 ? 2:45 ? 7:35 ? 5:48
?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? ? 7:94? pairwise comparison matrix
¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? ¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? Step 3. attributes can be de?ned using Equation (4) and
¼?3:08; 3:79; 4:32? is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
assessment attributes. The procedure environmental
fuzzy weights of each criterion with respect to different
¼?3:08; 3:79; 4:32? ? 5:48 ? 7:94?
determined by following the same procedure discussed above. Using the criterion LC 11 , plastics, as an example, ?rst the fuzzy Step 3. Equation (5). This is referred to as Similarly, we can obtain the remaining ~ r i , namely: be constructed for different experts. A synthetic pairwise comparison
Use the synthetic pairwise
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
comparison. A similar matrix asrisk ratings, in
¼?3:08; 3:79; 4:32? in Equation (2) contrast
¼?3:08; 3:79; 4:32? comparison matrix from Step 2. The fuzzy should to the regular weightings for different
Similarly, we can obtain the remaining ~ r i , namely: geometric mean (~ r i ) and fuzzy weights of each criteria.
. دنوش يم ه دا د شيامن 8 لو دج ر د fuzzy environmental
¼?3:08; 3:79; 4:32?
evaluation matrix of the environmental risk assessment is constructed by the pairwise comparison of the different assessment criterion ( ~ w i ) are de?ned using Equations (4) and (5) 1 ~ w i ¼?Lw i ; Mw i ; Uw i ? (6)
The rating of each attributed EA i can be expressed
Similarly, we can obtain the remaining ~ r i , namely: respectively: following format, analogous to Equation (6):
matrix can then be calculated in the
~ r 2 ¼?1:58; 2:05; 2:56? using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
~ r 1 ¼?~ a 11 5~ a 12 5~ a
Similarly, we can obtain the remaining ~ r i , namely:
~ r 2 ¼?1:58; 2:05; 2:56? 13 5~ a 14 5~ a 15 ? 5 ? 5
1
ناوت يم ،هباشم روط هب
~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15
attributes using triangular fuzzy numbers. The linguistics scales for the environmental assessment are described in Table 7. زا ه دافتسا اب ار يزاف يطيحم ت??سيز ک??سير را دقم ناوت يم سپ??س Similarly, we can obtain the remaining ~ r i , namely: 1=n ? (4)
fuzzy weights of each
? criterion
~ r 2 ¼?1:58; 2:05; 2:56? with respect to different environmental attributes can be de?ned using Equation (4) and
:مينک هبساحم زين ار رگي د ياه ~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
1=n
1=5 (4)
~ r 2 ¼?1:58; 2:05; 2:56?
(8)
Again, by incorporating all expert evaluations, the synthetic pairwise comparison matrix of the criterion with respect to ه دا د شيامن 9 لو د??ج ر د زين جياتن و درک هب??ساحم )5( و )4( يا??ه هل داعم (5). This is referred to 1=5 ; ?1 ? 2:45 ? 7:35 ? 5:48 1=5 ?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? 1=5 ?
¼ ?1
?
¼ ?1 ? 1:41 as fuzzy
~ r 3 ¼?0:35; 0:42; 0:52? ? 6:32 environmental risk ratings, in contrast to the regular weightings for different criteria.
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
1=5
~ r 2 ¼?1:58; 2:05; 2:56?
1 ? 1:41 ? 6:32 ? 4:47 ? 6:93?
EA i ¼?LEA i ; MEA i ; UEA i
Equation ?
f
1=5 ; ?1 ? 2:45 ? 7:35 ? 5:48 ? 7:94?
defuzzi?ed) weight value of the i-th criterion (w i ) is given as:
~ r 2 ¼?1:58; 2:05;
~ r 2 ¼?1:58; 2:05; 2:56? 2:56? ? 4:47 ? 6:93?
?1 ? 7:94?
?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49?
~ r 2 ¼?1:58; 2:05; 2:56? 5~ a 12 5~ a 13 5~ a 14 5~ a 15 ? 5
~ r 1 ¼?~ a 11
the assessment attributes is calculated and the results are shown in Table 8. ،هچراپکي ياهرايعم ينزو را درب زا . دنا ه دش ~ r 2 ¼?1:58; 2:05; 2:56? ~ 5~ a 14 5~ a 15 ? 5 1 ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? (5) ? (5)
?1 The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6):

~ r 1 ¼?~ a 11 5~ a 12 5a 13
¼?3:08; 3:79; 4:32?
In ranking the environmental assessment
? attributes,
~ r 3 ¼?0:35; 0:42; 0:52? the ?nal synthetic decision can be made and the resulting fuzzy
?
¼?3:08; 3:79; 1=5
~ r 2 ¼?1:58; 2:05; ; ?1
The fuzzy environmental risk ratings can then be calculated with Equations (4) And (5) and the results are shown in Table 9. يزاف کسير ياه ي دنب هبتر و ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? ¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? 1=5 ; ?1 1=5 ?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? 1=5 1=5 ? (7)
~ r 4 ¼?0:75; 0:96; 1:23? 4:32?
~ r 3 ¼?0:35; 0:42; 0:52?
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
1=5
~ r 3 ¼?0:35; 0:42; 0:52? 2:56? ? 2:45 ? 7:35 ? 5:48 ? 7:94?
¼ ?1 ? 1:41
synthetic decision matrix ER can be computed as:
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
~ r 5 ¼?0:28; 0:32; 0:39? ? 6:32 ? 4:47 ? 6:93?
f
Similarly, we can obtain
~ r 4 ¼?0:75; 0:96; 1:23? the remaining ~ r i , namely:
~ r 4 ¼?0:75; 0:96; 1:23? EA i ¼?LEA i ; MEA i ; UEA i ?
From the integrated criteria weight vector, ~ w, and fuzzy risk ratings, EA, the ?nal fuzzy synthetic decision can be made. The کي هجيتن . دروآ ت??س د هب ار يياهن يزاف يبيکرت باختنا ناو??ت يم ، f Similarly, we can obtain the remaining ~ r i , namely: ? 2:45 ? 7:35 ? 5:48 ? 7:94? ?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? (8)
f
The weight of each dimension can be calculated by Equation (5) as follows:
Step 5. (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
~ r 4 ¼?0:75; 0:96; 1:23?
¼?3:08; 3:79; 4:32?
Step 4. Since the calculation so far
~ r 5 ¼?0:28; 0:32; 0:39? involves linguistic variables, the next step is to defuzzify the weights to form meaningful

~ r 3 ¼?0:35; 0:42; 0:52?
result will be the fuzzy synthetic decision matrix ER calculated by Equation (9). For Criterion LC 11 (plastics), the fuzzy syn- هبساحم )9( ?ل داعم ساسارب هک ت??سا f يزاف يبيکرت باختنا سيرتام ~ r 5 ¼?0:28; 0:32; 0:39? ?gures for the analysis The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
(9)
ER ¼ EA5W
e
¼?3:08; 3:79; 4:32?
f
f
~ r 2 ¼?1:58; 2:05; 2:56?
In ranking the environmental
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
f 1 ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ? literature but Centre-of-Area (COA) is by far the most made and the resulting fuzzy
Similarly, we can obtain the remaining exist assessment attributes, the ?nal synthetic decision can be
popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each criterion (w i ) can be expressed in the
?gures for the analysis (e.g., ranking). Numerous methods
w 5 ¼?0:28; 0:32; 0:39? 2:56? in
~ r ~ r 2 ¼?1:58; 2:05; ~ r i , namely:
?1
The weight of each dimension can be calculated by Equation (5) as follows:

thetic decision matrix of EA 1 , “consumption of material, energy and other resources”, is expressed as: EA يزاف بيکرت باختنا سيرتام ،)اه کي ~تسلاپ( LC رايعم يارب . دوش يم The weight of each dimension can be calculated by Equation (5) as follows:
~ r 4 ¼?0:75; 0:96; 1:23? remaining ~ r i , namely:
Similarly, we can obtain the
synthetic decision matrix ER can be
comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
The weight of each dimensioncomputed as:
~ r 2 ¼?1:58; 2:05; 2:56? weights of each
? can be calculated by Equation (5) as follows: be expressed in the
1 form:
where W is the criteria weight vector calculated in the previous
11
f
1 popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy 1 step. followingcriterion (w 1i ) can ?
w
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
?1 ~ r 2 ¼?1:58; 2:05; 2:56?
;
;
?
?
Each
f 1 ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ?
UER ij , with
: دوش يم فيرعت تروص نيا هب »رگي د عبانم و يژرنا ،داوم فرصم« ينع ?ي ¼?3:08; 3:79; 4:32?5 4:32 ? / ?
?1 ¼ LER
?ij ;
MER ij ;
~ r 2 ¼?1:58; 2:05; 2:56?
f g
?1 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28 respect to the criterion LC ij
following form:element of the fuzzy synthetic decision matrix ER, ER ij
(9)
f
e
f
~ r 2 ¼?1:58; 2:05; 2:56?
f ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ?
1 f 1 r 5 ¼?0:28; 0:32; 0:39?
w ~ ~ r 3 ¼?0:35;
0:019; 0:046; 0:113? ? ?0:212; 0:404; 0:690? ER ¼ EA5W 1 0:42; 0:52? 1 fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and
w 1¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ?
can be estimated by the following equations: ; 1 ~ w i ¼?Lw i ; Mw i ; Uw i ? (6)
¼?3:08; 3:79; 4:32?5
4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
~ r 3 ¼?0:35; 0:42; 0:52?
?
¼?0:341; 0:503; 0:715? ; ?
(6)
~ r 2 ¼?1:58; 2:05; 2:56? ~ r 1 ¼?~ a 11 5~ a 12 5~ a 13 5~ a 14 5~ a 15 1 ? 5 1 1 1 1 1 ? ?
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
~ r 2 ¼?1:58; 2:05; 2:56
~
where W is the criteria weight vector
¼?3:08; 3:79; 4:32?5 each life-cycle phases can be obtained and the results are shown in Table 4.
Likewise, the remaining weights of calculated in the previous step.
)0.019, 0.046, 0.113( × )0.212, 0404, 0690( ¼?0:341; 0:503; 0:715? The weight of each dimension can ; be ; calculated by Equation (5) as follows: ?
;
~ w i ¼?Lw i ; Mw i ; Uw i ?
;
¼?3:08; 3:79; 4:32?5?
4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
~ r 4 ¼?0:75; 0:96; 1:23?
?
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6): (i.e.,
where Lw i ,Mw i ,Uw i represent the lower, middle and (10)
Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated. upper values of the fuzzy weight of the i-th criterion. The non-fuzzy
?
~ r 4 ¼?0:75; 0:96; 1:23?
?
LER ij ¼ LEA ij ? LW ij Each element of the fuzzy synthetic decision 1=5 ; ?1 ? 2:45 ? 7:35 ? 5:48 ? 7:94? ; 1=5 UER ij , with respect to the 1=5
Likewise, the remaining weights of each life-cycle phases can be obtained and the results are shown in Table ¼ LER ij ;
?1 ? 3:46 ? 7:94 ? 6:48 ? 8:49? criterion LC ij
f g
MER ij
~ r 3 ¼?0:35; 0:42; 0:52? ¼ ?1 ? 1:41 ? 6:32 ? 4:47 ? 6:93? matrix ER, ER ij
Taking the “procurement” phase as an example, the calculation is as follows: 4.
?1
~ r 5 ¼?0:28; 0:32; 0:39? the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of defuzzi?ed) weight value
Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated. of the i-th criterion (w i ) is given as:
can be estimated by the following equations:
¼?0:341; 0:503; 0:715?
~ r 3 ¼?0:35; 0:42; 0:52?
f ¼ ~ r 1 5?~ r 1 4 ~ r 2 4r 3 ?ل داعم زا ه دافتسا اب ناوت يم ار دعب ره نزو
: درک هبساحم تروص نيا هب )5(
(11)
¼?0:341; 0:503; 0:715? ~ 4~ r 4 4~ r 5 ?
Table 7 زا ه دافت??سا اب )0.004,0.019,0.078( تروص هب يزاف برض يبيرقت ?جيتن Likewise, the remaining weights EA i ¼?LEA i ; MEA i ; UEA i ?shown in Table 4. (8)
MER ij ¼ MEA ij ? MW ij
fand the results are shown in Table 4.
w 1 ¼?0:28; 0:32; 0:39?
½?Uw i ? Lw i ???Mw i ? Lw i ?? of each life-cycle phases can be obtained
defuzzi?ed) weight value of the i-th criterion
~ r 4 ¼?0:75; 0:96; 1:23? (w i ) is given as:
Taking the “procurement” phase as an example, the calculation is as follows:
Likewise, the remaining weights of each life-cycle phases can be obtained and the results are
~ r 5 ¼?3:08; 3:79; 4:32?
The weight of each dimension can
? Lw i be calculated by Equation (5) as follows:
1
1
3 (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
Linguistic scales for environmental risk assessment. Using the COA method dimension can be calculated by Equation (5) as follows: 1 ? (7)
?
~ r 4
The weight of each
w 1 ¼ ¼?0:75; 0:96; 1:23?
Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
LER ij ¼ LEA
را دقم ،COA شور زا ه دافتسا اب . ديآ يم ت??س د هب )12( ات )10( ياه هل داعم Taking ¼?3:08; 3:79; 4:32?5 ; ; (12) (10)
Similarly, we can obtain the remaining ~ r i , namely:
~ r 5 ¼?0:28; 0:32; 0:39? ij ? LW ij
½?Uw i ? Lw i ???Mw i ? Lw i ?? the “procurement” phase as an example, the calculation is as follows:
w 1 ¼???Mw i ? Lw i ??=3 ? Lw
(7)
UER ij ¼ UEA ij ? UW ij
? Lw
4:32
? 0:341 ? / ? 0:39 3:79 ? /
¼ i i
?0:715 ? 0:341? ? ?0:503 ? 0:341?
Fuzzy number Linguistic terms Scale of fuzzy number w i ¼ ½?Uw i ? Lw i 3 Taking the “procurement” phase as an example, the calculation is as follows: ? 0:32 3:08 ? / ? 0:28
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
?1
~ r 5 ¼?0:28; 0:32;
?1
The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
f ¼ ~ r 1 5?~ r 1 4 0:39?
3 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ?
،يهبا??شم روط هب . درک هب??ساحم 0.034 تروص هب ناوت يم ار نآ يزافريغ ~ r 2 w 1 ¼?1:58; 2:05; 2:56? Step 5. as follows: (11)
w 1
f ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 Equation (5)
The weight of each dimension can be calculated by
MER ij ¼ MEA ij ? MW ij
synthetic decision matrix ER can be computed as:
?0:715 ? 0:341? ? ?0:503 ? 0:341? ½?Uw i ? Lw i ???Mw i ? Lw i ?? 4~ r 5 ?
The weight
w 1 ¼ ¼?0
½?Uw i ? Lw i ???Mw i ? Lw i ?? Lw i be calculated by Equation (5) as follows:
~ 1 Equal (1, 1, 1) Step 5. The next step is to calculate 3 the environment risk ratings of different criteria with respect to the ?ve environmental
¼ 0:520 of each dimension can Equation (7).
Finally, ER has
¼ to be defuzzi?ed using the COA method given by
1
f ?
1
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
?
?
1
3
? 0:341:341; 0:503; 0:715?
f
? Lw i 1
1
?
?
?1 3:79; 4:32?5
w 1 ¼
;
~ 2 Weak high (1, 2, 3) طبترم EA و EA ، EA ، EA ? د??نام يقاب يطيحم يبايزرا ?صخ??شم 4 ~ r 2 ¼?1:58; organisational performances of ;individual criteria e 1 (12) (9)
;
f are also assessed. Using
UER ij ¼ UEA ij ?the
Similar to the environmental assessment,
3 4:32?5 4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
;
¼?3:08; 3:79;
ER ¼ EA5W Equation (2) should be constructed for different experts. A synthetic pairwise comparison
¼ 0:520 f ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ? 1 to Step 4 and the key difference is simply the object of the pairwise
?0:715 ? 0:341? ? ?0:503 ? 0:341? comparison. A similar matrix as in be obtained and the results are shown in Table 4.
Likewise, the remaining weights of each life-cycle phases can
¼?3:08; 2:05; 2:56?
3
2
f
w 1
? 0:3410:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
?1
~ 3 Moderate high (2, 3, 4) 5 4 assessment attributes. The procedure is similar to Step UW ij 3 OP i can be expressed in the following format:
4:32 ? / ?
the same FAHP approach, the rating of each
? attributed
w 1
¼ ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 4~ r 4 4~ r 5 ?
? 0:341 then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
f
¼ the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
?0:715 ? 0:341? ? ?0:503 ? 0:341?
?
~ r 3 ¼?0:35; 0:42;
~ 4 Slightly high (3, 4, 5) ت??س د هب 0.013 و 0.008 ،0.017 ،0.011 تروص هب ناوت يم ار LC ا??ب Using ¼?0:341; 0:503; 0:715? ? 1 matrix can 1 where W is the criteria weight vector calculated in the previous step.
1 0:52?
~
11
1
¼?0:341; 0:503;
1
1
¼ 0:520 defuzzi?ed using the COA method given by Equation (7).
fuzzy weights of each criterion with respect to different environmental attributes
matrix can then be calculated using the geometric to be
?
Finally, ER has
;
;
30:715?
¼?3:08; 3:79; 4:32?5 mean method outlined in Step 2. Thereafter, the fuzzy geometric mean
4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
f
~ 5 High (4, 5, 6) ET ENERGY T DAY ر د لقتسم ياهرايعم اب طبترم يطيحم ک??سير ي دنب هبتر يارب جياتن . دروآ Taking the “procurement” phase as an example, the calculation is as follows: and f g ? can be de?ned using Equation (4) and
¼?3:08; 3:79; 4:32?5
?
¼ 0:520 remaining weights of each life-cycle phases can be obtained and the results are shown in Table 4.
;
Likewise, the
;
H.K. Chan et al. / The British Accounting Review 46 (2014) 344e360
351
MER ij ;
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28 and criteria are also assessed.
Likewise, the remaining weights of each life-cycle phases can be obtained and the results are shown in Table 4. Using
Similar to the environmental assessment, the organisational performances of individual
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
~ r 4 ¼?0:75; 0:96; 1:23?
~ 6 Quite high (5, 6, 7) Iran Energy News Agancy fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) UER ij , with respect to the criterion LC ij
¼?0:341; 0:503; 0:715? COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
Using the
Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase
the same FAHP approach, the rating of each attributed
½?Uw i ? Lw i ???Mw i ? Lw i ?? regular weightings for different criteria. format:
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the OP i can be expressed in the following
can be estimated by the following equations: can be calculated.
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6):
~ 7 Very high (6, 7, 8) دوبهب يارب مهم ياه ه دو دحم ? دنه د نا??شن و ب??سانم تايح ?خرچ زاف ره Taking the “procurement” phase as an example, the calculation is as follows:
¼?0:341; 0:503; 0:715?
Taking the “procurement” phase as an example, the
? Lw i calculation is as follows:
~ r 5 ¼?0:28; 0:32; 0:39?
w 1 ¼ of each life-cycle phases can be obtained and the results are shown in Table 4.
Likewise, the remaining weights the following format, analogous to Equation (6):
~ 8 Extremely high (7, 8, 9) The rating of each attributed EA i can be expressed in (13) 3 can be calculated by Equation (5) as follows: (10)
. دنتسه حرط
Likewise, the remaining weights of each life-cycle phases can be obtained and the results are shown in Table 4.
The weight of each dimension
LER ij ¼ LEA ij ? LW ij can be calculated.
f
~ 9 Absolutely high (8, 9, 9) OP i ¼?LOP i ; MOP i ; UOP i ? Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase (8)
f
w 1 ¼ COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
EA i ¼?LEA i ; MEA i ; UEA i ?
½?Uw i ? Lw i ???Mw i ? Lw i ??
Using the
Taking the “procurement” phase as an example, the calculation is as follows:
يبيکرت يجوز ?سياقم سيرتام ناوت يم ،ناسکي شور کي زا ه دافتسا اب Taking the ¼ ~ r 1 5?~ r 1 4 ~ r 2 4~ r 3 ?1 ? Lw i ? 0:341 MER ij ¼ MEA ij ? MW ij (8) (11)
?0:715 ? 0:341? ? ?0:503 ? 0:341?
½?Uw i ? Lw i ???Mw i ? Lw i ?? ? Lw i
f
EA i ¼?LEA i ; MEA i ; UEA i ?
w 1 ¼
¼ “procurement” phase as an example, the calculation is as follows:
w 1
3
3 3 4~ r 4 4~ r 5 ?
f
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
?0:715
In ranking the organisational performance assessment attributes, the ?nal synthetic decision can ناوت يم ار تا??يح ?خرچ زاف ره زا ه دنام يقاب يا??ه نزو ،سا??سا نيمه رب 1 ? (12)
. دروآ تس د هب ينامزاس درکلمع يبايزرا ياه هصخشم اب طبترم ياهرايعم زا ار be made and a resulting
?0:715 ? 0:341? ? ?0:503 ? 0:341? ? 0:341 1
1
?
½?Uw i ? Lw i ???Mw i ? Lw i ?? ? 0:341? ? ?0:503 ? 0:341?
;can
synthetic decision matrix ER can be computed as:
¼ 0:520? Lw i i ???Mw i ? Lw i ?? decision
¼ ½?Uw i ? Lw . دنا ه دش ه دا د شيامن 4 لو دج ر د ،جياتن هک دروآ تس د هب ; and the resulting
? 0:341 be made
In ranking the environmental assessment attributes, the ?nal synthetic
UER ij ¼ UEA ij ? UW ij fuzzy
¼
w 1 ¼
3
f
fuzzy synthetic decision matrix OR can be computed as follows: synthetic decision matrix ER can be computed as: ¼?3:08; 3:79; 4:32?5 4:32 ? / ? 0:39 3:79 ? / ? 0:32 3:08 ? / ? 0:28
ياه هل داعم قيرط زا ار يزاف ينامزاس درکلمع ياه ي دنب هبتر ناوت يم سپس
3
? Lw i
f
3 w 1 ¼
3
f
¼ 0:520
ER ¼ EA5W
?0:715 ? 0:341? ? ?0:503
f
e
¼?0:341; 0:503;
f
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
? 0:341
. دنا ه دش ه دا د ناشن 10 لو دج ر د زين جياتن هک دز نيمخت )5( و )4( يزاف ياه نزو يزاف ي د ري داقم ،)7( ?ل داعم و COA شور زا ه دافتسا اب f (9)
¼ 0:520 ? 0:341? 0:715?
¼
?0:715 ? 0:341? ? ?0:503 ? 0:341?
(14)
? 0:341
OR ¼ OP5W ER ¼ EA5W Likewise, the remaining weights of each life-cycle phases can be (9)
f
f
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
e
»يزاس ه دامآ« زاف نتفرگ رظنر د اب .تسا ه??سياقم لباق ،تايح ?خرچ زاف ره obtained and the results are shown in Table 4.
3 ¼
e
f
f
~
3
where W is the criteria weight vector calculated in the previous step.
ياه ي دنب هبتر و يرا??يعم نزو ?چراپکي را درب يزاف بر??ض قيرط زا Using the COA method (Equation (7)), the non-fuzzy value of the fuzzy weights of each life-cycle phase can be calculated.
¼ 0:520
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
~
?
¼ 0:520 previous step.
where W is the criteria weight vector calculated in the : دوب دهاوخ تروص نيا هب هبساحم ،هنومن ناونع هب f g ? MER ij ; UER ij , with respect to the criterion LC ij
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
Taking the “procurement” phase as an example, the calculation is as follows:
( يزاف
طبترم ) f g يبيکرت ميمصت سيرتام ناوت يم ،يزاف ينامزاس درکلمع
?
?
?
Each element of the fuzzy synthetic decision matrixOR, OR ij ¼ LOR ij ; MOR ij ; UOR ij , with respect to the criterion LC ij ? MER ij ; UER ij , with respect to the criterion
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
f g
can be estimated by the following equations: LC ij
can be estimated by the following equations:
can be estimated by the following equations: ناوت يم ار يزاف برض يبيرقت ?جيتن . دروآ تس د هب زين ار نامزاس درکلمع اب ½?Uw i ? Lw i ???Mw i ? Lw i ??
w 1 ¼ 3 ? Lw i LER ij ¼ LEA ij ? LW ij (10)
ري داقم و هبساحم جياتن . دروآ تس د هب )17( ات )13( ياه هل داعم زا ه دافت??سا اب (15)
LOR ij ¼ LOP ij ? LW ij LER ij ¼ LEA ij ? LW ij ?0:715 ? 0:341? ? ?0:503 ? 0:341? MER ij ¼ MEA ij ? MW ij (10) (11)
يبايزرا جياتن هباشم . دنا ه د??ش ه دا د ناشن 11 لو دج ر د اهنآ ? د??ش يزاف ي د ¼ 3 ? 0:341 (11)
MOR ij ¼ MOP ij ? MW ij MER ij ¼ MEA ij ? MW ij ¼ 0:520 (16) (12)
تايح ?خرچ فلتخم ياهزاف اب طابترا ر د ينامزاس درکلمع نازيم ،يطيحم UER ij ¼ UEA ij ? UW ij
UER ij ¼ UEA ij ? UW ij (12)
(17)
UOR ij ¼ UOP ij ? UW ij . دنتسه يحارط دوبهب مهم ياه هزوح ? دنه د ناشن ،اهنآ اب طبترم ياهرايعم و ر د اهنآ لامرن را دقم و تا??يح ?خرچ ياهزاف مامت زا يزافريغ نزو ر??ي داقم
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
f
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
يطيحم تسيز کسير و ينامزاس درکلمع نازيم ،لااب لاور سا??سارب ار هخرچ زاف ره ر د اهرايعم نزو ،هباشم روط هب . دنا ه دش ه دا د نا??شن 5 لو دج
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
f
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
تايح ?خرچ ر د لقتسم ياهرايعم اب طبترم يبايزرا ?صخ??شم ره يعمجت the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
Again, OR has to be defuzzi?ed using the COA method. the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
ره يارب ار يّلک نازوا تاعلاطا زا يا هصلاخ 6 لو دج . دروآ تس د هب ناوت يم
f
ه دش ه دا د شيامن 5 لکش ر د هلئ??سم نيا . دنتسه هب??ساحم لباق ،لوصحم
The objective of the above procedures is to analyse the weighing (i.e., contribution) of each criterion and life-cycle phase to . دنک يم هئارا ،يبتارم هلسلس ل دم ر د رصنع
the overall LCA. The FAHP method can also be used for the selection of design improvement alternatives. Below is the case
و )OP ( تيفيک ،ينامزا??س درکلمع يبايزرا ياه هصخشم نايم ر د .ت??سا
صخاش 5 اب طابترا ر د فلتخم ياهرايعم يطيحم تسيز کسير ري داقم
2
study to illustrate how the FAHP method can be used in a real-life application in relation to green product development.
لوصحم تيهام هک دنت??سه مهم ?صخ??شم نيمو د و نيلوا ،)OP ( هنيزه
3 . دنا ه دش صخشم ، دن دش فيصوت لااب ر د هک يا هيور ساسارب يطيحم يبايزرا
5. Case study يبايزرا ?صخشم 5 نايم ر د . دنزا??س يم صخ??شم هعلاطم ر د ار صخ??شم
يبايزرا سيرتام ا دتبا ،کيتسلاپ ، LC ياهرايعم زا ه دافت??سا اب لاثم يارب
11
The product in this case study is a personal electronic product as reported in Yung et al. (2011). The manufacturer of the
تايح ?خرچ فلتخم ياه زاف يارب يزافريغ ياه نزو -5 لو دج
تايح ?خرچ فلتخم ياه زاف يارب يزاف ياه نزو -4 لو دج
product attempted to initiate an environmentally friendly product design program with the aim of developing a tool (i.e., LCA)
to help the designers select the best product design options. In this study, we refer to the case to demonstrate how the Mw Uw
Lw
لامرن ياه نزو
يزافريغ ياه نزو
proposed model can simplify new product development in a “green” perspective. It is not our intention to repeat the LCA for i i i
the product and the LCA results are not discussed in this paper. The proposed model instead aims to help screen out the 0.503 0.715
0.341
0.493
0.520
w 1
design options for a subsequent LCA.
0.275
0.290
0.175
The overall objective is de?ned for the design selection following the procedures outlined in Section 3. The next and most 0.272 0.424
w 2
challenging step is to choose the criteria against which the alternatives will be evaluated. With reference to the case (Yung 0.056 0.087
0.060
0.039
0.057
w 3
et al., 2011), the key criteria in each phase are identi?ed and the hierarchy of the LCA-based AHP is constructed as shown in
Table 2 (only the selected criteria are shown here for demonstration purposes). If a full LCA has not been developed, the 0.128 0.204
0.131
0.083
0.138
w 4
related information should be collected according to the procedures outlined in Section 3.
0.031
0.046
0.043
Thereafter, the FAHP method is used to assign comparative ratings of environmental performance to the different designs 0.042 0.064
w 5
being assessed. The ?rst step (Step 1 in Section 4) is to construct a pairwise comparison among the criteria from different
experts. The consistency ratio of each judgement is simultaneously calculated and checked to ensure that it is lower than or
equal to 0.1.
87
ريذپ دي دـجت ياه يژرنا و
Table 2 مو د ?رامش لوا لاس
An example of hierarchy structure for LCA based green design selection.
Life-cycle phases Criteria Assessment criteria
LC 1 . Procurement LC 11 . Plastic: general (ABS, PE, etc.) Environmental Assessment Attributes
LC 12 . Plastic: special (rubber, high impact, etc) EA 1 . Consumption of material, energy and
LC 13 . Metal other resources
LC 14 . Electronic component (resistors, capacitors, EA 2 . Emission to air, water or soil
LCD, etc) EA 3 . Anticipated pollution
LC 15 . Printed Circuit Board (PCB) EA 4 . Generation of waste material
LC 2 . Production LC 21 . Surface mount EA 5 . Possibility of re-use, recycling, and
LC 22 . Die bonding recovery of materials and/or energy
LC 23 . General assembly Organisational Performance Attributes
LC 24 . Metal processing (stamping, etc) OP 1 . Time
LC 25 . Plastic processing (injection, etc) OP 2 . Quality
LC3. Packaging LC 31 Packaging: product level OP 3 . Cost
LC 32 . Packaging: carton level OP 4 . Flexibility
LC 33 . Manual
LC4. Distribution LC 41 Transportation
LC 42 . Storage
LC5. End-of-life LC 51 . Extent of recyclability
LC 52 . Extent of reuse
LC 53 . Extent of recovery