Page 87 - مجله مدیریت سبز - شماره 2 - نسخه فلش

Step 2. 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
proposed by Buckley (1985): The proposed methodology uses the advantages of fuzzy set theory developed by Zadeh in the 1960s that can incorporate
imprecise and uncertain variables (Zadeh, 1965). A major advantage of FAHP is in assessing each environmental output and
Step 2. Since 1 2 E ? 1=E the organisational performance of a design with different criteria in linguistic terms (e.g., high, very high) or assigning a fuzzy
? the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
(3)
~ a ij ¼ ~ a 5~ a 5…5~ a
different experts ij ij number instead of a precise numerical value, which is sometime impossible to obtain. A fuzzy number is a special fuzzy set
ij to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
Step 2.
Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
~
such that A ¼ {(x, m A (x), x 2 R)}, where the value of x lies on the real line R/[0, 1] and m A (x) is the fuzzy membership function
يارب نيون ياــهراکهار 1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only
~ one expert in Step
of x associated to the fuzzy set A.Wede?ne a fuzzy number A on R to be a triangular fuzzy number (TFN) as the most
نيگنايم . دينک ه دافتسا يبيکرت يجوز ?سياقم سيرتام زا و 2 ماگ زا :3 ماگ the evaluation of different experts would lead to different
يــناخرچزاب و تــيري دم proposed by Buckley (1985): Step 2. Since تيوضع عبات هک مينک يم فيرعت ،نآ ي دربراک لکش نيرت لوا دتم ناونع هب matrices, we need to integrate the opinions of
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric
commonly used form. The membership function can be described as: mean method
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
proposed by Buckley (1985): experts would lead to different
زا ه دافتسا اب بيترت هب )
Since
8 matrices, we need to integrate the opinions
Step 2.
يتعنص ياه دحاو ر د بآ Since the evaluation of different experts would lead to different matrices, we need to integrate the opinions of :زا تسا ترابع نآ of
Step 2.
? the evaluation of different
( رايعم ره يزاف ياه نزو و ) ( يزاف يس دنه
< ?x ? L?=?M ? L?; x2½L; M? (~ r i ) and fuzzy weights of each
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean
Step 3.
1=E
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
?
E
1
different experts to form one synthetic form one
different experts to
~ a ij ¼ ~ a 5~ a 5…5a synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
? ~ comparison matrix. This step is unnecessary if there is only one expert in Step
2 pairwise
(3)
?U ? x?=?U ? M?; x2½M; U? )1(
witteveenandbos.com criterion ( ~ w i ) are de?ned using : دنوش يم فيرعت )5( و )4( ياه هل داعم m A ?x?¼ different experts would lead to different matrices, we need to integrate the opinions of (1)
ij
ij
ij
? 1=E proposed by Buckley (1985):
1 Equations (4) and (5) respectively: of
Since the evaluation
Step
E2. (~ a ij ) are calculated by using the geometric mean method
2
1. The elements of the synthetic pairwise
1. The elements of the synthetic pairwise comparison matrix comparison matrix (~ a ij ) are : would lead to different matrices, we need to integrate the opinions of (3)
~ a ij ¼ ~ a 5~ a 5…5~ a Since the evaluation of different experts calculated by using the geometric mean method
ij Step 2.
otherwise
ij
ij
0;
different experts to
? form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
proposed by Buckley (1985): Buckley (1985):
? 1=E
)4(
26413997 :نارهترتف د proposed by 1=n different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step (3)
2
1
(4)
E
The superscript in Equation
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? (3) is the index referring to different experts with a total of E experts.
~ a ij ¼ ~ a 5~ a 5…5~ a pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
1. The elements of the synthetic
ij pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
1. The elements of the synthetic
ij
ij
نارک رگنايب زين L ،لااب نارک ? دنه د ناشن U .تسا L < M < U ،عبات نيا ر د
1=E
? ? 1=E The superscript in Equation (3) is the index referring to different experts with a total of E experts.
proposed by Buckley (1985):

1
2
~ a ij ¼ ~ a 5~ a 5…5~ a E ij ? 1 2 E ? ?1 proposed by Buckley (1985): (3) (3)
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
Step 3. ~ a ij ¼ ~ a 5~ a 5…5~ a
ij
ij
.تسا يزاف د دع را دقم نيرت لمتحم ? دنه د ناشن زين M نينچمه ،نيياپ
(5)
ij
ij
ij
Step 3.
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of eachE experts.
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? ? 1 2 The superscript in Equation (3) is the index referring to different experts with a total of
? 1=E
)5(
? 1=E
1 (5) respectively:
E
?
E
Since the evaluation of different experts would lead
criterion ( ~ w i ) are de?ned using Equations (4) and 5…5~ a ij 2 سايقم کي .تخا??س صخ??شم ?=( L,M,U( اب ناوت يم ار TFN opinions of (3) (3)
~ a ij ¼ ~ a ij 5~ a ij
Step 2.
~ a ij ¼ ~ a 5~ a 5…5~ a to different
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: matrices, we need to integrate the
ij
ij
ij
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
Step 3.
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
1=n synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
different experts to form one
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to (4)
1=n criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: form meaningful
فيرعت عون نيا زا .تسا ه دش هئارا 1 لو دج ر د زين اه تيولوا زا يزاف يثلثم
The superscript in Equation
، دوب يملاک ياهريغتم لما??ش ،شخب نيا ات تاب??ساحم هک اجنآ زا :4 ماگ (3) is the index referring to different experts with a total of E experts.
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
Step 3. Use the synthetic pairwise comparison matrix from Step (4)
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each geometric mean method
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
Step 3.
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the mosteach
Step 3.
Step 2.
را دانعم ماقرا ليک??شت يارب يزاف تلاح زا اه نزو ن درک جراخ ي دعب ?لحرم lead to different matrices, we need to integrate the opinions of
Since the evaluation of different experts would
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: ،ينا??سنا يملاک حلاطصا 9 اب اهرايعم اي تايح ?خرچ زاف 2 ???سياقم يارب
proposed by Buckley (1985):
?1
1=n
criterion ( ~ w (4)
criterion ( ~ w i ) are de?ned using Equations
Step i ) and (5) respectively:
(5)
?1 are de?ned using Equations (4) and (5) respectively:
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? 2004). Assume the fuzzy weights of each criterion (w i ) can be expressed in the (~ r i ) and fuzzy weights of each
popular and easy to use (e.g., Hsieh et al., 3. Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (5) (4)
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
ي د دعتم ياه شور هچرگا صوصخ نيا ر د .ت??سا ي دنب هبتر و ليلحت يارب
following form:
(4)
1. The elements of
1=n
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? matrix (~ a ij ) are calculated by using the geometric mean method
1=n ~ pairwise comparison
2
~ a ij ¼ ~ a 5~ a 5…5a
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? 1=n ? 1 the synthetic E ij ? 1=E criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: . دوش يم ه دافتسا (4) (3) (4) (5)
?1
اه شور نيرت ه داس و نيرت بوبحم اجنيا ات هيحان ِزکرم شور اما ، دنرا د دوجو
ij
ij
تسا ه دش يزاس دنتسم تاقيقحت ر د يبوخ هب FAHP درا دناتسا دنيارف
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
proposed by Buckley (1985): ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
1=n next step is to defuzzify the weights to form meaningful
Step 4. Since the calculation so far involves linguistic variables, the
?1
?1
(5)
(5)
(6)
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? experts would lead to different matrices, we
Since the evaluation of different
Step 2.
ياه نزو هک دينک ضرف .)2004 ،ناراکمه و هي??س ،لاثم يارب( تسا ه دوب need to integrate
~ w i ¼?Lw i ; Mw i ; Uw i ? ?1 matrices, we need to integrate the opinions of the opinions of
Step 2. Since the evaluation of different experts would lead to different 1=E ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? و هي??س قيقحت سا??سارب ،مو??سرم ياه لاور زا يا هصلاخ ،ريز ياه ماگ و is by far the most (4)
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
(5)
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) far the most
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? Equation (3) is the index referring to different experts with a total of E experts.
?1 is only one expert in Step
Step 2. pairwise comparison
different experts to form one synthetic
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
E matrix. This step is unnecessary if there
2
The superscript in ?
?
~ a ij ¼ ~ a 5~ a 5…5~ a step is unnecessary if there is only one expert in Step
different experts to form one synthetic pairwise comparison 1 the evaluation of different experts would lead to different matrices, we need to integrate the opinions of (3) (5)
Sincematrix. This
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
: درک فيصوت ريز لکش هب ناوت يم ار ) ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? fuzzy weights of each criterion (w i ) can be expressed in the
ij
ij
ij
popular and easy to use (e.g., Hsieh et al., 2004). Assume far
:تسا )2004( ناراکمه form meaningful
Step 4. Since the calculation so
( رايعم ره يزاف the involves linguistic variables, the next step is to defuzzify the weights to
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
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.,
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
Step 3. comparison matrix (~ a ij ) are calculated by using the geometric mean method
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful one expert in Step
1. The elements of the synthetic pairwise
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) Since ?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
Step 2. are calculated by using the geometric mean method
following form:the evaluation of different experts would lead to different matrices, we need to integrate the opinions of
following form:
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
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
1. The elements of the synthetic pairwise comparison matrix
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but (~ a ij ) are calculated by using the geometric mean method
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
proposed by
proposed by Buckley (1985): Buckley (1985): defuzzi?ed) weight value of the i-th criterion (w i ) is given as: et al., 2004). Assume the fuzzy weights of each criterion (w i ) can be
popular and easy to use (e.g., Hsieh Centre-of-Area (COA) is by far the most is only one expert in Step
ناوت يم . دينک داجيا ،ناگربخ هورگ زا ار يجوز ?سياقم ياه سيرتام :1 ماگ expressed in the
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there
The superscript in Equation (3) is the index
Step form: referring to
following form: different experts with a total of E experts.
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
proposed by Buckley (1985):
~ w i ¼?Lw i ; Mw i ; Uw i ? 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
popular and easy to use (e.g., Hsieh et al., 2004). Assume synthetic pairwise )هربخ ره يازا ه??ب( سيرتام نياربانب ، درک ه دافت??سا يملاک يا??هريغتم زا (6)
1. The elements of the
)6( of each criterion (w i ) can be expressed in the geometric mean method
following the fuzzy weights comparison matrix (~ a ij ) are calculated by using the
(6)
1=n
(7)
?gures for Assume the fuzzy weights of each criterion (w i ) can be expressed in the (4)
following form: popular and easy to use (e.g., Hsieh et al., 2004).
? ? 1=E w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
proposed
~ w i ¼?Lw i ; Mw i ; Uw i ? 5…5~ a in ?
E 1
1
? ? 1=E 2 E ~ r i ¼?~ a i1 5~ a i2 by Buckley (1985):
~ w i ¼?Lw i ; Mw i ; Uw i ? from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
~ a ij ¼ ~ a 5~ a 5…5~ a a 5~ a 5…5~ a ij Step 3. 2. Use the synthetic pairwise comparison matrix lead to different matrices, we need to integrate the opinions of (6) (6)
(3)
2 ~ a ij ¼ ~
? 1=E different experts would
Since the evaluation of
(3)
Step
ناگربخ صخاش ،يزاس ه داس يارب . دش دهاوخ داجيا )2( ?ل داعم سا??سارب
?
ij ij
ij
E
popular and easy to use (e.g., Hsieh
1
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., ) can be expressed in the
ij
ij
~ a ij ¼ ~ a
following form: 5~ a 5…5~ a
~ w i ¼?Lw i ; Mw i ; Uw i ? et al., 2004). Assume the fuzzy weights of each criterion (w i
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: (3) (5)
ij
?1 pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
? 1=E
different experts
ij to form one synthetic
ij
Step 5. 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.,
where
The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
1
E
2
?
(6)
following form:
(3)
where
نزو ينايم و لااب ،ن??يياپ ري داقم ? دنه د نا??شن Lw i ,Mw i ,Uw i represent the lower, middle and
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
~ a ij ¼ ~ a ij 5a ij
~ w i ¼?Lw i ; Mw i ; Uw i ? ~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? ~ 5…5~ a ij هل داعم نيا ر د 2 calculated by using the 3 upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are
2 geometric mean method
where Lw i ,Mw i ,Uw i represent the lower, middle and
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
:) دينيبب ار 2 ?لحرم( مينک يم فذح ،شخب نيا ر د ار د دعتم 3
The superscript in Equation (3) is the index referring
defuzzi?ed) weight value of the i-th E experts.
~ w i ¼?Lw i ; Mw i ; Uw i ? to different experts with a total of
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: criterion (w i ) is given as:
The superscript in Equation (3) is the index referring to different experts 1=n with a total of E experts. 1 with a total of E experts. 1 ~ a 12 / ~ a 1n (6) (4)
proposed by Buckley (1985):
و يزاف تلاح زا ه دش جراخ( ? دش يزاف ي د نزو را دقم . دنتسه مُا i رايعم يزاف
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?(3) is the index referring to different experts
The superscript in Equation
~ a 12
~ a 1n
defuzzi?ed) weight value of the i-th criterion
3 (w i ) is given as:
1 pairwise comparison
/ experts. A synthetic
comparison. A similar matrix as in Equation (2) should be constructed for differentThe non-fuzzy
where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of the fuzzy weight 2 6 ~ a 21 step is to defuzzify the weights to form meaningful (7) (7) (6)
6 ~ a 21 (i.e.,
Step 4. Since the calculation so far involves linguistic variables,
1
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i Uw i ? of the i-th criterion. with a total
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 the
1 next
~ w i ¼?Lw i ; Mw i ; referring to different experts
7 of E experts.
The superscript in Equation (3) is the index
7
~ a 12 weights of each
~ ~ a 2n
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy
Step 3.
~ ? Lw i
Step 3. Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean w i ¼ ½?Uw i ? Lw in Step «Step 2. mean (~ r i « 4 5 criterion. The non-fuzzy (7) (7)
matrix can then be calculated using the geometric mean method outlined in each
~ a 2n 7
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i (~ r i ) and fuzzy weights of
« weights of each
defuzzi?ed) weight value of the i-th criterion the lower, middle and upper values of the
Use the synthetic pairwise comparison matrix from Step
4 fuzzy weight of the i-th ) and fuzzy
1
7 )2( (i.e.,
Step 3.
/ 1 Thereafter, the fuzzy geometric mean and
( مُا i رايعم زا )يعطق د دع هب ه دش لي دبت 2. The fuzzy geometric
~ a 1n A ¼ 6 7
A ¼ 6
? 1=E
:تسا حرش نيا هب ) (w i ) is given as: Numerous methods exist
?gures for the analysis (e.g., ranking).
where Lw i ,Mw i ,Uw i represent ?1
6 ~literature but Centre-of-Area (COA) is by far the most
?
« 5
1
E
Use
(5)
2
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? the synthetic pairwise comparison matrix from
Step
The next step is to calculate the environment i ???Mw i
~ risk ratings of different criteria with respect to the ?ve environmental
~ a ij ¼ ~ a 5~ a
1 ? Lw i ??=3 ? Lw i
criterion ( ~ w i ) are de?ned using Equations (4) and (5) 5…5a
1 (3)
Step 5. 3. ~
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively: respectively: Step 5. (4) and (5) respectively: A ¼ 6 a 21 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
4 lower, middle and upper values of the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
where Lw i ,Mw i ,Uw i represent the
The next step is to calculate the environment risk ratings of different criteria with respect
/ to the ?ve environmental
« 5 1
ij
ij
« attributes
1 /can be de?ned using Equation (4) and
ij
fuzzy weights of each criterion with respect to different environmental
defuzzi?ed) weight value of the i-th criterion (w i ) is given as:
criterion ( ~ w i ) are de?ned using Equations
~ a 2n 7
~ a n2of each criterion
~ a n1 (w i ) can be expressed in the
~ a n2
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
~ a n1
w i ¼ ½?Uw i ? Lw popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights / (w i ) is given as: (7)
The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
defuzzi?ed) weight value of the i-th criterion
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
1
Step 5. i ???Mw i ? Lw i ??=3 ? Lw i
following form:
The next step is to contrast
~ a n1 calculate the environment risk ratings of different criteria with respect to the ?ve environmental
Step 5.
~ a n2 to the regular weightings for different criteria.
1=n
comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
1=n 1=n Equation (5). This is referred to as fuzzy environmental risk ratings, in (7)
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
(4)
)7(
1=n
(4)
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? referring to different experts with a total of E experts.
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? (3) is the index
The superscript in Equation
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6): to form meaningful
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? 5~ a i2 5…5~ a in ? Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights (4) (4)
~ r i ¼?~ a i1
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
Step 5.
ET ENERGY T DAY comparison. A similar matrix as in Equation (2) should be constructed for different هل داعم نيا ر د (6) (7)
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i experts. A synthetic pairwise comparison
comparison. A similar matrix
و ~ a ij ¼ 1=~ a ji a ij ¼ 1=~ a ji and for different experts. A synthetic pairwise comparison
fuzzy weights of each criterion with respect to different environmental attributes (COA) is by
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area
~ can be de?ned far the most
where (2) should be constructed using Equation (4) and
?1matrix from Step 2. The fuzzy geometric
Step 3.
Use the synthetic pairwise comparison
where ~ a ij ¼ 1=~ a ~ as in Equation ~ ) and fuzzy weights of each
~ w i ¼?Lw i ; Mw i ; Uw i ?
~ ji a ij ¼ 1=~ a ji and attributes can be de?ned using Equation (4) and
?1
Iran Energy News Agancy
?1
The next step is to calculate the environment risk ratings of different criteria mean (r i
matrix can then be calculated using the geometric mean method outlined in Step 2.
where ~ a ij ¼ 1=~ a ji a ij ¼ 1=~ a ji and Thereafter, the fuzzy geometric mean and
fuzzy weights of each criterion with respect to different environmental with respect to the ?ve environmental (5)
~ w i ¼ ~ r ?1 assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise (5)
(5)
(5)
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
Step 5.~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
Equation (5). This is referred to as fuzzy environmental risk A synthetic pairwise comparison can be expressed in the
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ? i 5?~ r 1 4…5~ r n ? f and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each criterion (w i )
(8)
criterion
popular ( ~ w i ) are de?ned using
Step 5. and (5) respectively:
comparison. A similar matrix as in Equation (2) Equations (4) The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
8 regular weightings for different criteria.
EA i ¼?LEA i ; MEA i ; UEA i ? should be constructed for different experts. the key difference is simply
8ratings, in contrast to the the object of the pairwise
assessment attributes. The procedure is similar to Step 1 to Step 4 and
ياهرايعم زا طيحم کسير ياه ي دنب هبتر ?بساحم ،ي دعب ?لحرم :5 ماگ
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6):
fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and
where Lw i ,Mw i ,Uw i represent the lower, middle and upper values of
8 the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and
~ ~ ~ to Step 1 to Step 4 and the key difference is simply the object of the pairwise
assessment attributes. The procedure is similar
> ~ ~ ~ ~ ~
following form:
> 1; 3; 5; 7; 9
> 1; the fuzzy geometric mean and
if criterion i is relatively important to criterion j
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, 1; 3; 3; 5;format, analogous to Equation (6):
> ~ ~ ~
if criterion i is relatively important to criterion j criterion j
if criterion i is relatively important to
~ ~ ~ 5; ~ 7; 9 7; 9
comparison. A similar matrix as in Equation (2) should be constructed for different
The rating of each attributed EA i can be expressed in the following experts. A synthetic pairwise comparison
> weightings for different criteria.
> contrast to the regular :دشاب رت مهم ، j رايعم اب هسياقم ر د i رايعم رگا
هيور نيا .تسا يطيحم ت??سيز يبايزرا ياه هصخ??شم اب طبترم فلتخم
1=n
> the weights to form meaningful
Equation (5). This is referred the next step is to defuzzify
Step 4. Since the calculation so far involves linguistic
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: variables,
> to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
(4)
f ¼?LEA i ; MEA i ; UEA i ? the next
>
> Equation (2) should be constructed for different experts. A synthetic pairwise comparison
Step 4. Since the calculation so far involves linguistic variables,
Equation (5). This is referred to as fuzzy environmental risk ratings, in step is to defuzzify the weights to form meaningful
comparison. A similar matrix as in
(8)
> > > > > < < de?ned using Equation (4) and
In ranking the environmental assessment attributes, the ?nal synthetic decision can be
< made and the resulting fuzzy
fuzzy weights of each criterion with respect to different environmental attributes can be
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
EA i
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ?
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful ~ a ij ¼ method outlined in Step 2. Thereafter, the fuzzy geometric mean and
if i ¼ j
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the
1 fuzzy geometric mean and most
if i ¼ j i ¼ j
11 EA i can be expressed in the following format, analogous to Equation (6):
if analogous to Equation (6): far the most
The rating of each attributed the geometric mean (COA) is by
matrix can then be calculated using
The rating of each attributed EA i can be expressed in the following format, Centre-of-Area
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but
(6)
EA i ¼?LEA i ; MEA i ; UEA i ? as: contrast to the regular
f f ديلک فلاتخا و تسا 4 ات 1 ياه ماگ هباشم
~ a ij ¼ ¼ weightings for different criteria.
> attributes can be de?ned using Equation (4) and (7)
:دشاب ربارب ، j اب i رگا
fuzzy weights of each criterion with respect to different environmentalA) is
popular and exist in literature
دياب .تسا يجوز ?سياقم ،نآ ي ???Mw i ? Lw i ??=3 but Centre-of-Area (CO
synthetic decision matrix ER can be computed in Lw i al., 2004). Assume far the most by far the most
~ w i ¼?Lw i ; Mw i ; Uw i ?
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area ~ a ij the fuzzy weights of each criterion (w i ) can be expressed in the (8)
w i ¼ ½?Uw i ? Lw i easy to use (e.g., Hsieh
Equation (5). This is referred to as fuzzy environmental risk ratings, ? et (COA) is by
?gures for the analysis (e.g., ranking). Numerous methods?1
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy weights of each
> 1 1 1 1 1
fuzzy weights of each criterion with respect criterion (w i )
(5)
> can be expressed in the
1 1 1 1 1 1 1 to different environmental attributes can be de?ned using Equation (4) and
>
> 1 1 1 (6):
The rating of each attributed EA i can be expressed in the following format,
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
following form:
Equationس . دوش داجيا فلتخم ناگربخ يارب )2( ?ل داعم هبا??شم سيرتام کي
سپ al., 2004).
criteria.
f f (5). This is referred to as fuzzy environmental risk ratings, in contrast to
> > > > > : ~ ~ ~ 5 ~ 7 ~ ; regular weightings for
popular and easy to use (e.g., Hsieh et
f fuzzy weights fuzzy weights of each criterion (w i )
f ER can be computed can
; ; ; ; the
> as: be expressed in the
if criterion i is relatively less important to criterion j
> ; ; ; ;different
if criterion i is relatively less important to criterion j
ER ¼ EA5W ; MEA i ; UEA i ? of each criterion (w i ) can be expressed in the
popular and easy to use (e.g., Hsieh et al., 2004). Assume the e Assume the synthetic decision matrix fanalogous to Equation 9 synthetic decision can be made and the resulting fuzzy (8)
if criterion i is relatively less important to criterion j
>
> ; ; ;
(8)
(9)
following form:
>
EA i ¼?LEA i ; MEA i ; fuzzy
Equation (5). This is referred to as
: ratings, in contrast to the regular weightings for different criteria.
: UEA i ? environmental risk
~ ~ ~ ~ ~
1 3 ~ ~ ~ ~ ~ of the i-th criterion.اب هسياقم ر د i رايعم رگا
In ranking the environmental assessment attributes, the ?nal criteria with respect to theThe non-fuzzy (i.e.,
:دشاب رت تيمها مک ، j رايعم
EA i ¼?LEA i next step is to calculate the environment risk ratings of different
1 3 5 7 9
The rating of each attributed EA i can be
ER expressed in the following format, analogous to Equation (6):
Step 5. i ,Uw i
following form: following form: where Lw i ,Mw Therepresent the lower, middle and upper values of the fuzzy weight 1 3 5 7 9 ?ve environmental (9)
EA5 e W
f rating of each attributed EA i can be expressed in the following format, analogous to Equation (6):
Theم سيرتام کي ناوت يم
(8)
f ¼ f
(6)
assessment attributes. The procedure is similar to Step 1 to next step is to defuzzify the weights to form meaningful
Step 4. Since the calculation so far involves
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: the
~ w i ¼?Lw i ; Mw i ; Uw i linguistic variables,
EA i ¼?LEA i ; MEA i ; UEA i ? synthetic decision matrix ER can be computed as: Step 4 and the key difference is simply the object of the pairwise
يس دنه نيگنايم شور زا ه دافتسا اب ار يجوز ?سياق ?
f
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
? synthetic decision can be made and the resulting fuzzy
In ranking the environmental assessment attributes, the ?nal
where W is the criteria weight vector calculated in the previous step. in the previous step. (6)
~ ~ w i ¼?Lw i ; Mw i ; Uw i ?
where ~ W is the criteria weight vector calculated for different experts.
? A synthetic pairwise comparison
f دنه نيگنايم ناوت يم سپس . درک هبساحم ، د??ش فيصوت 2 ماگ ر د هک be constructed
?gures for the analysis (e.g., ranking). Numerous methods f but Centre-of-Area (COA) is by far the most (8)
يس comparison. A similar matrix as in Equation (2) should exist in literature
f ; UEA i ? ,Uw i represent the lower, middle and upper values of the fuzzy weight (6)
ER ¼ EA5W
where Lw
f g decision matrix f g ¼ LER ij ;of the i-th criterion. The non-fuzzy (i.e.,
(7)
e
ER, ER
Each element
?
?
f of the fuzzy synthetic
f
MER ij ; ij the resulting fuzzy
~ w i ¼?Lw i ; Mw i ; Uw i ? Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; (6) MER ij ; UER ij , with respect to the criterion (9) (8)
synthetic decision matrix ER can be computed as:
UER ij
matrix can then be calculated using the geometric mean method
synthetic decision matrix ER can be computed as: , with respect to the criterion LC ij LC ij
~ w i ¼?Lw i ; Mw i ; Uw i ? In ranking the environmental assessment i ,Mw i EA i ¼?LEA i ; MEA i ; UEA i ? be made and 2. Thereafter, the fuzzy geometric mean and
w i ¼ ½?Uw i ? Lw i (e.g., Hsieh et al., 2004).
popular and easy to use
EA i ¼?LEA i ; MEA i ???Mw i ? Lw i ??=3 ? Lw i Assume the fuzzy weights of each
f attributes, the ?nal synthetic decision can outlined in Step criterion (w i ) can be expressed in the
f ,Uw i represent the lower, middle and upper values of the fuzzy
يطيحم تسيز ياه هصخشم اب ار طبترم رايعم ره يزاف ياه نزو و يزاف (w i ) is given
defuzzi?ed) weight value of the i-th criterion
Step 2.
دوجو هب ار ي د دعتم ياه سيرتام ،فلتخم ناگربخ يبايزرا هک اجنآ زا :2 ماگ evaluation of different experts would lead to different matrices, we need to integrate the opinions of
Since the
~ following equations:
synthetic decision matrix ER can be computed as: can be estimated by the following equations: as: weight of the i-th criterion. The non-fuzzy (i.e., (9)
where Lw i ,Mw i
can be estimated by the each criterion with respect to different
f environmental attributes can be de?ned using Equation (4) and
fuzzy weights of
ER ¼ EA5W
where W is the criteria weight vector calculated in the previous step.
following
f form:
e
In ranking the environmental assessment attributes, the ?nal the resulting fuzzy
f
defuzzi?ed)
(9)
? non-fuzzy (i.e.,
In ranking weight upper values of the fuzzy weight of
f the value of the i-th criterion (w i ) is given as: the i-th criterion. The
where Lw i ,Mw i ,Uw i represent the lower, middle and
Equation (5). This is referred to as fuzzy environmental ratings of different (i.e.,
where Lw i ,Mw i ,Uw i represent the lower, middle and ER ¼ EA5W environmental assessment attributes, the ?nal synthetic decision can be made and ? synthetic decision can be made and the resulting fuzzy
The next step is to calculate the environment risk
f g criteria with respect to the ?ve environmental
Step 5. upper values of the fuzzy weight of the i-th criterion. The non-fuzzy
?سياقم سيرتام کي ليکشت يارب ار فلتخم ناگربخ هاگ دي د دياب ، دروآ يم form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
e
e اب ه??سياقم ر د . درک فيرعت ،)5( و )4( يا??ه هل داعم زا ه دافت??سا اب فلتخم risk ratings, in contrast to the
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3
different experts to criteria.
(10)
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; regular weightings for different
(7)
MER ij ;
(9)
ER ¼ EA5W
LER ij ¼ LEA ij ? LW ij ? Lw i
synthetic decision matrix ER can be computed as:
(10)
f
assessment attributes. given as:
defuzzi?ed) weight value of the i-th criterion
~ matrix ER can be computed as:
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: (w i ) is f synthetic decision 1 f UER ij , with respect to the criterion LC ij
f
~ The rating of each The procedure is similar to Step
can be estimated by the following equations: the following format, analogous to Equation (6): object of the pairwise
where W is the criteria weight vector calculated in the previous step.
LER ij ¼ LEA ij ? LW ij attributed EA i can be expressed in to Step 4 and the key difference is simply the
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
(6)
(7)
(11)
where W is the criteria weight vector calculated in the previous step.
ياه ي دنب هبتر هب هلئسم نيا ،توافتم رايعم ره يارب يلومعم ياه يه د نزو
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
~ w i ¼?Lw i ; Mw i ; Uw i ?
MER ij ¼ MEA ij ? MW ij
f g the ?ve environmental
? ratings of different criteria with respect to
?
?
The next step is to calculate the environment risk
e Step 5.
f be constructed for different experts. A synthetic pairwise comparison
f similar matrix as in Equation
comparison. A
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
where W is the criteria weight vector calculated in the previous (2) should e لوا ماگ ر د سانشراک کي طقف هک يتروص ر د .مينک هچراپکي ،يبيکرت يجوز MER ij ; UER ij , with respect to the criterion LC ij
ER ¼ EA5W
proposed by Buckley (1985):
(9)
~
f step.
(9)
(11)
UER (7)
?
f
MER ij ¼ MEA ij ? MW ij synthetic decision matrix ER, ER ij ¼ LER ij ; (7)
assessment
MER ij ;
can be estimated by 1 to Step 4 and the key difference is simply the object of the pairwise
Each element of the fuzzy attributes. The procedure is similar to Step
Since the evaluation of different experts would
?سياقم سيرتام رصانع . دوب دهاوخن يرورض هلحرم نيا ، دشاب هتشا د دوجو lead to different matrices, we need to integrate the opinions of
(8)
ER ¼ EA5Wf g
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
matrix can then be calculated usingthemiddle
MER ij ;of different criteria with respect to the ?ve environmental
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i where صيصخت f ره ي دنب هبتر .تسا هتسباو يزاف يطيحم ت??سيز کسير Step 2.the following equations: ij , with respect to the criterion LC ij(12) (10)
EA i ¼?LEA i ; MEA i ; UEA i ? the environment risk
Step 5. Lw i ,Mw i ,Uw i represent the lower,
Each element of the fuzzy synthetic decision matrix ER, geometric mean ratingsof the fuzzy weight of the i-th criterion. The non-fuzzy (i.e.,
f g and upper values
The next step is to calculate
LER ij ¼ LEA ij ? LW ijER ij ¼ LER ij ; method outlined in Step 2. Thereafter, the fuzzy geometric mean and
UER ij ¼ UEA ij ? UW ij
?
?
UER ij , with respect to the criterion LC ij
comparison. A similar matrix as
can be estimated by the following equations: in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
~
E This step is unnecessary if there is only one expert in Step
?
where W is the criteria weight vector calculated in the previous step. the pairwise
2 (4) and
? using Equation
defuzzi?ed) weight value of
can be estimated by the following equations: the i-th criterion (w i is given as: different experts to form one synthetic pairwise comparison matrix. ? 1=E (3)
ER to different environmental attributes can be de?ned
fuzzy weights of each criterion with respect to)
where W is the criteria weight vector calculated Step 1 to Step 4 and the
assessment attributes. The procedure is similar
~ in the previous step. key difference is simply the object of
1
(12)
( يبيکرت يجوز
،)6( ?ل داعم ا??ب ه??سياقم لباق تروص هب و ريز تمرف هب ناوت يم ار ه??تفاي
طسوت ي داهنشيپ يس دنه نيگنايم شور زا ه دافتسا اب )~ a ij ¼ ~ a 5~ a 5…5~ a
Finally, f has to be defuzzi?ed using the COA method given by Equation (7).
MER ij ¼ MEA ij ? MW ij using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric
matrix can
UER ij ¼ UEA ij ? UW ijthen be calculated
The next step is to calculate the environment risk ratings of different criteria with
f g ?ve environmental environmental
Step 5.
ij
Step 5. The next step is to calculate the environment risk ratings of different criteria with respect to the respect to the ?ve UER ij , with respect to the MER ij ; ij mean and ? ij (11) (10)
?
?
1. The elements of the synthetic pairwise comparison matrix (~ a ij ) are calculated by using the geometric mean method
LER ij ¼ LEA ij ? LW ij ; synthetic decision can be made and the resulting fuzzy
comparison. A similar matrix as in Equation (2) should be constructed for
MER ij ;
In ranking the environmental assessment attributes, the ?nal different experts. A synthetic pairwise comparison
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij contrast to the regular weightings for different criteria.
f g
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
UER ij , with respect to the criterion LC ij
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; criterion LC ij
fuzzy weights of each criterion with respect to different
Equation (5). This is referred to as fuzzy environmental risk ratings, in environmental attributes can be de?ned using Equation (4) and
w i ¼ ½?Uw i ? Lw
(7)
assessment attributes. The procedure is similar to Step 1 to Step 4 and 1 to Step ? Lw i ??=3 can be estimated by the following equations: be expressed in the following format: and (10) (12) (11)
: دنوش يم هبساحم ،)1985( يلکاب
synthetic decision the key difference key difference is simply the object
: درک فيصوت
LER ij ¼ LEA ij ? LW ij matrix ER can be computed as: the object of the pairwise of the pairwise
can be estimated by the following equations: is simply
(10)
matrix can then be calculated using the geometric mean method outlined in Step
Equation (5). This is referred to as fuzzy environmental risk ratings, 2. Thereafter, the fuzzy geometric mean
assessment attributes. The procedure is similar to Step i ???Mw i
f 4 and the ? Lw i
the same FAHP approach, the rating of each attributed OP i can
LER ij ¼ LEA ij ? LW ij of
The rating
proposed by Buckley (1985): to Equation (6):
MER ij ¼ MEA ij ? MW ij analogous to the regular weightings for different criteria.
feach attributed EA i can be expressed in the following format, in contrast
UER ij ¼ UEA ij ? UW ij the COA method given by Equation (7).
Finally, ER has to be defuzzi?ed using
The superscript in Equation (3) is the index referring to different experts with a total of E experts.
comparison. A similar matrix as in Equation
comparison. A similar matrix as in Equation (2) should be (2) should be constructed for different experts. A synthetic pairwise comparison (11) (11)
fuzzy weights constructed for different experts. A synthetic pairwise comparison
f of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and
The
MER ij ¼ MEA ij ? MW ij each attributed EA i can be expressed in the following format, analogous to Equation (6):
f rating of
Step 5.
MER ij ¼ MEA ij ? MW ij ER ¼ EA5W calculate the environment risk ratings of different
? criteria with respect to the ?ve environmental
1=E criteria are also assessed. Using
Similar to the environmental assessment, the organisational performances of individual
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter,
e
LER ij ¼ LEA ij ? LW ij the fuzzy
fas fuzzy environmental risk ratings, in contrastgeometric mean
Equation method outlined
LER ij ¼ LEA ij ? LW ij to in Step 2. Thereafter, the fuzzy geometric mean and
matrix can then be calculated using the geometric mean The next step is to f procedure is similar to Step 1 to Step a ij ¼ ~ a 5~ a 5…5~ a E and )3( (10) (9) (10) (12) (3)
1 to the
f (5). This is referred
2regular weightings for different criteria.
?
UER ij ¼ UEA ij ? UW ij
(8)
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
Step 3. of the pairwise
assessment attributes. The
~ the key difference is simply the object
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
)8( 4 and
ij in the following format:
the same FAHP approach, the rating of each attributed OP i can be expressed
EA i ¼?LEA i ; MEA i ; UEA i ?
ij
ij
(8)
fuzzy weights of each criterion with respect
MER environmental environmental attributes can be de?ned using Equation (4) and
(11)
(12)
The rating of each attributed EA i can be expressed in the following format,
(12)
fuzzy weights of each criterion with respect to different ~ to different EA i ¼?LEA i ; MEA i ; UEA i ? MER ij ¼ MEA ij ? MW ij step. analogous to Equation (6): criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
UER ij ¼ UEA ij ? UW ij ij ¼ MEA ij ? MWattributes can be de?ned using Equation (4) and
where W is the criteria weight vector calculated in the previous
(11)
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
UER ij ¼ UEA ij ? UW ij ij as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
comparison. A similar matrix
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
?
?
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; different criteria.
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria. UER ij , with respect to the
MER ij ;
f
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format: criterion LC ij
ره ?رامش هب هراشا ،)3( ?ل داعم ر د يبيکرت يجوز ?سياقم ره يلااب ياه هرامش fuzzy
f g
matrix
f can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting
EA i ¼?LEA i ; MEA i ; UEA
The superscript in Equation (3) is the index referring to different experts with a total of E experts. opinions of
UER ij ¼ UEA ij ? UW ij 2.
(8)
Since the evaluation of different experts would lead to different matrices, we need to integrate the
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
Step
(12)
can be estimated by the following equations:
UER ij following format, analogous to Equation (6): to
The rating of each attributed EA i can be expressed in the following format, analogous
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
The rating of each attributed EA i can be expressed in the f ¼ UEA ij ? UW ij f،يطيحم يبايزرا ياه هصخشم ي دنب هبتر ر د Equation (6): ~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? 1=n (12) (4)
يياهن يبيکرت ميمصت ناوت يم i ?
ER to different environmental attributes can
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). be de?ned using Equation (4) and
fuzzy weights of each criterion with respect
f
synthetic decision matrix ER can be computed as: computed as:
synthetic decision matrix f can be
.دوش يم متخ E د دع هب دا دعت ،عومجم ر د هک درا د هربخ in the following format:
different experts to form one synthetic pairwise comparison matrix. This step is unnecessary if there is only one expert in Step
the same FAHP approach, the rating of each attributed OP i can be expressed
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
Step 3. performances of individual criteria are also assessed. Using
f as fuzzy environmental risk ratings,
Similar to the environmental assessment, the organisational in contrast to the regular weightings for different criteria.
Equation (5). This is referred to
Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
In ranking
f the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
(9)are calculated by using the geometric mean method
f LER ij ¼ LEA ij ? LW ij W
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
ER ¼ EA5W
(9)
EA i ¼?LEA
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
(8)
ER ( يزاف ميمصت يبيکرت سيرتام و درک ذاختا ار 1. The elements of the synthetic pairwise comparison matrix (~ a ij
f : درک هبساحم نينچنيا ار ) f ¼ EA5 e
f
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
EA i ¼?LEA i ; MEA i ; UEA i ? i ; MEA i ; UEA i ? The rating of each attributed EA i can be expressed in the following format, analogous (8) (10) ) ?1 (5)
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). to Equation (6):
e
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
f
f
synthetic decision matrix ER can be computed as: proposed by Buckley (1985): يملاک سايقم تيوضع عبات -1 لو دج
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
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 (11)
where ~ W is the criteria weight vector calculated in the previous step.
MER ij ¼ MEA ij ? MW ij
~
1=n OP i can be expressed in the following format:
the same FAHP approach, the rating of each attributed
(8)
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
?
(9)
? ER, ER ij 1 fuzzy resulting
)9(the resulting the
~ r i ¼?~ a i1 5~ a i2 5…5~ a in ? fuzzy
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and be made and ? 2 MER ij ; ? 1=E ? UER ij , with respect to the criterion LC ij (4)
In ranking the environmental assessment attributes, the ?nal synthetic decision can
where W is the criteria weight vector calculated in the previous step. g ¼ LER ij ;
Each element of the fuzzy synthetic decision matrix f ?
f
E يناسنا ملاک حلاطصا
f f
EA i ¼?LEA i
يزاف د دع
ER ¼ EA5W ; MEA i ; UEA i ?
e
يزاف د دع سايقم
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; ~ a 5~ a 5…5~ a
UER ij ¼ UEA ij ? UW ij by the following equations:
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
(12)ij
ij
ij
synthetic decision matrix ER can be computed as: computed as: can be estimated f g ~ a ij ¼ ij MER ij ; UER ij , with respect to the criterion LC (3)
synthetic decision matrix ER can be
f
where W is the criteria weight vector calculated
f
~
can be estimated by the following equations: in the previous step.
In ranking the environmental assessment attributes, the ?nal
?gures for the analysis (e.g., ranking). Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
?1 ربارب
? synthetic decision can
?be made and the resulting fuzzy
)1,1,1(
UER
(9)
ER ¼ EA5W ER ¼ EA5W synthetic decision matrix ER can be computed as: f g The superscript in Equation (3) is the index referring to (10) (5)
~ w i ¼ ~ r i 5?~ r 1 4…5~ r n ?
Each element of
(9)
f the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
LER ij ¼ LEA ij ? LW ij
MER ij ;
لبق ?لحرم ر د ه??ک ت??سا را??يعم نزو را در??ب ک??ي ،ه??ل داعم ن??يا ر د
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). ij , with respect to the criterion LC ij different experts with a total of E experts.
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
e
e f
f
f
f
f
can be estimated by the following equations: )1,2,3( فيعض حيجرت following form: (10)
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
(11)
LER ij ¼ LEA ij ? LW ij MER ij ¼ MEA ij ? MW ij
اب ت??سا ربارب يزاف م??يمصت يبيکرت سيرتام ر??صنع ره .د??ش هب??ساحم
(9)
ER ¼ EA5W
~
where W is the criteria weight vector calculated in the
~
where W is the criteria weight vector calculated in the previous step.previous step. ? Step 3. Use the synthetic pairwise comparison matrix from Step 2. The fuzzy geometric mean (~ r i ) and fuzzy weights of each
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
f
Step 4. Since the calculation so far involves linguistic variables, the next step is to defuzzify the weights to form meaningful
e
f
(11)
(12)
criterion ( ~ w i ) are de?ned using Equations (4) and (5) respectively:
(10)
MER ij ¼ MEA ij ? MW ij ¼ UEA ij ? UW ij
?
)2,3,4(
Each element of the fuzzy synthetic decision
زا کيره نياربانب .
ياه f g matrix ER, ER ij ¼ LER ij ;
?
MER ij ;
?
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; MER ij ; UER ij , with respect to the criterion LC ij ح ّ جرم ًاتبسن ~ w i ¼?Lw i ; Mw i ; Uw i ? in literature but Centre-of-Area (COA) is by far the most (6)
~
?gures for the analysis (e.g., ranking). Numerous methods exist
UER ij , with respect to the criterion LC ij
where W is the criteria weight vector calculated in the previous step.
LER ij ¼ LEA ij ? LW ij f
UER ij g
(11)
can be estimated by the following equations:
can be estimated by the following equations: Each element of the fuzzy ij f g 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
(12)
1=n
?
?
UER ij ,
: دز نيمخت ريز ياه هل داعم زا ه دافتسا اب ناوت يم ار LC ياهرايعم اب طبترم
(4)
MER ij ¼ MEA ij ? MW ij
MER ij ;
Finally, f synthetic decision matrix ER, ER ij ¼ LER ij ;
UER ij ¼ UEA ij ? UW ij ER has to be defuzzi?ed using the COA method given by Equation (7). ? with respect to the criterion LC ij
~ r i ¼?~ a i1 5~ a i2 5…5~ a in حيجرت لباق
)3,4,5(
can be estimated by the following equations: following form: 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.,
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
(10)
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
LER ij ¼ LEA ij ? LW ij
LER ij ¼ LEA ij ? LW ij UER ij ¼ UEA ij ? UW ij ~ w i ¼ ~ r i 5?~ r 1 4…5~ ?1 (10) (12) (5)
)4,5,6(
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). r n ? بوخ defuzzi?ed) weight value of the i-th criterion (w i ) is given as:
f
(10)
)10(
LER ij ¼ LEA ij ? LW ij
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using (6)
(11)
~ w i ¼?Lw i ; Mw i ; Uw i ?
MER ij ¼ MEA ij ? MW ij
MER ij ¼ MEA ij ? MW ij Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). (11) (7)
بوخ ًاتبسن
f
)5,6,7(
(11)
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
Step 4. Since the calculation so far involves
MER ij ¼ MEA ij ? MW ij
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format: linguistic variables, the next step is to defuzzify the weights to form meaningful
)11(
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using

(12)
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.,
(12)
?gures for the analysis (e.g., ranking).
UER ij ¼ UEA ij ? UW ij
UER ij ¼ UEA ij ? UW ij the same FAHP approach, the rating of each attributed OP i can be expressed in the following format: Numerous methods exist in literature but Centre-of-Area (COA) is by far the most
بوخ رايسب
(12)
UER ij ¼ UEA ij ? UW ij )6,7,8( Step 5. The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
defuzzi?ed) weight value of the i-th criterion (w i ) is given as: weights of each criterion (w i ) can be expressed in the
)12( popular and easy to use (e.g., Hsieh et al., 2004). Assume the fuzzy
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). by Equation (7). following form: assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
Finally, ER has to be defuzzi?ed using the COA method given
(7)
f
f
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
f
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using assessed. Using comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
Similar to the environmental assessment, the organisational performances of individual criteria are also
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
(6)
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format: Step 5. ~ w i ¼?Lw i ; Mw i ; Uw i ? matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of the pairwise
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.,
85
ريذپ دي دـجت ياه يژرنا و Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
comparison. A similar matrix as in Equation (2) should be constructed for different experts. A synthetic pairwise comparison
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6):
مو د ?رامش لوا لاس defuzzi?ed) weight value of the i-th criterion (w i ) is given as:
matrix can then be calculated using the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
(7)
w i ¼ ½?Uw i ? Lw i ???Mw i ? Lw i ??=3 ? Lw i
fto different environmental attributes can be de?ned using Equation (4) and
fuzzy weights of each criterion with respect (8)
EA i ¼?LEA i ; MEA i ; UEA i ?
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
Step 5. The next step is to calculate the environment risk ratings of different criteria with respect to the ?ve environmental
The rating of each attributed EA i can be expressed in the following format, analogous to Equation (6): the pairwise
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
assessment attributes. The procedure is similar to Step 1 to Step 4 and the key difference is simply the object of
synthetic decision matrix ER can be computed as: synthetic pairwise comparison
comparison. A similar matrix as in Equation (2) should be constructed f for different experts. A
EA i ¼?LEA i ; MEA i ; UEA i ? the geometric mean method outlined in Step 2. Thereafter, the fuzzy geometric mean and
matrix can then be calculated using (8)
f
ER ¼ EA5W
fuzzy weights of each criterion with respect to different environmental attributes can be de?ned using Equation (4) and (9)
f
f
e
Equation (5). This is referred to as fuzzy environmental risk ratings, in contrast to the regular weightings for different criteria.
In ranking the environmental assessment attributes, the ?nal synthetic decision can be made and the resulting fuzzy
~
where W is the criteria weight vector calculated in the previous step.
The rating of each attributed f EA i can be expressed in the following format, analogous to Equation (6): ? ?
synthetic decision matrix ER can be computed as:
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; MER ij ; UER ij , with respect to the criterion LC ij
f g
EA i ¼?LEA i ; e can be estimated by the following equations: (8) (9)
f
f
f
ER ¼ EA5W MEA i ; UEA i ?
~
In ranking the environmental assessment attributes, the ?nal synthetic
where W is the criteria weight vector calculated in the previous step. decision can be made and the resulting fuzzy (10)
LER ij ¼ LEA ij ? LW ij
?
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ;
synthetic decision matrix ER can be computed as: f g ? MER ij ; UER ij , with respect to the criterion LC ij (11)
f
MER ij ¼ MEA ij ? MW ij
can be estimated by the following equations:
ER ¼ EA5W (9)
e
f
f
UER ij ¼ UEA ij ? UW ij (12)
~
where W is the criteria weight vector calculated in the previous step. (10)
LER ij ¼ LEA ij ? LW ij
? ?
Each element of the fuzzy synthetic decision matrix ER, ER ij ¼ LER ij ; MER ij ; UER ij , with respect to the criterion LC ij
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). (11)
f g
MER ij ¼ MEA ij ? MW ij
can be estimated by the following equations: f
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
(12)
UER ij ¼ UEA ij ? UW ij the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
LER ij ¼ LEA ij ? LW ij (10)
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7). (11)
MER ij
f ¼ MEA ij ? MW ij
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
(12)
UER ij ¼ UEA ij ? UW ij
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format:
Finally, ER has to be defuzzi?ed using the COA method given by Equation (7).
f
Similar to the environmental assessment, the organisational performances of individual criteria are also assessed. Using
the same FAHP approach, the rating of each attributed OP i can be expressed in the following format: