Efficiency Determination of the Forest Sub

Transkript

International Journal of Fuzzy Systems, Vol. 16, No. 3, September 2014
358
Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data
Envelopment Analysis (Case Study: Denizli Forest Regional Directorate)
İsmail Şafak, Altay Uğur Gül, Mehmet Emin Akkaş, Mustafa Gediklili,
Ş. Mümtaz Kanat, and S. Ümit Portakal
Abstract1
weighted inputs [1].
DEA was developed in order to measure and compare
Until this study an efficiency evaluation study had the technical efficiency of the public institutions on the
not been carried out down to the level of forest basis of article on efficiency measurement of Farrell by
sub-districts in Turkey. In this research, it is aimed to Charnes et al [2, 3]. Today DEA is used in many fields
evaluate the efficiency of the forest sub-districts in such as production, service and finance.
the Denizli Forestry Regional Directorate using fuzzy
In DEA models, values of all input and output data of
data envelopment analysis (Fuzzy DEA) for years aimed decision units must be exactly known [4]. In other
2007 and 2009. Fuzzy DEA solutions were carried out words, the one or more missing values in inputs and
using the data range. Fuzzy data was established by outputs data set cannot be used in DEA models. In most
defining the lower, central and upper limits on the models of practice DEA in literature, efficiency measbasis of the triangular membership function. These urements is executed the assumption that is known for
data are converted into interval data considering the certain all data whose aimed input and output variables
approach of Zimmermann (1991) α cutting set. Thus, [5]. Because, in production process, all data aimed input
the upper and lower limits of efficiency values were and output cannot be always fully measured [6]. In such
obtained at five different α (0; 0.25; 0.50; 0.75 and cases, for certainly immeasurable data in production
1.00) using fuzzy data envelopment analysis. Then process, the uncertainty theory plays an important role in
inefficient forest sub-districts were listed from best to DEA models [7].
worst using the Minimax Regret-Based Approach.
In 1965, Lotfi A. Zadeh [8] laid the foundation of the
fuzzy logic by proposing the definition of fuzzy sets
Keywords: Forest sub-districts, efficiency, fuzzy data where qualifications are expressed with the graded
envelopment analysis, Denizli.
membership function instead of the classical sets where
qualifications are expressed with the binary membership
1. Introduction
function. Later in the period, fuzzy thought system developed by Zadeh, has been widely used in the develData envelopment analysis (DEA) is one of the meth- opment of fuzzy models. Due to play a more important
ods used for measuring the efficiency using a large and realistic role in evaluating the efficiency of decision
number of inputs and outputs variables. DEA have been units, fuzzy DEA models covering fuzzy numbers are
evaluated the efficiency of the decision units by the sum developed [9]. Sengupta has published the first study on
of weighted outputs by comparing with the sum of fuzzy DEA [10]. In this article, Sengupta has redesigned
the standard DEA model by making fuzzy the conCorresponding Author: İsmail Şafak is with the Department of Forest straints and objective function in case of uncertain data
Management and Economics, The Aegean Forestry Research Institute, using the fuzzy linear programming model [11, 12].
İzmir, Turkey.
Later in the period, DEA studies have been focused on
E-mail: [email protected]
Altay Uğur Gül is with the School of Tobacco Expertise, Celal Bayar how to convert data with fuzzy value into data with precise value and how to incorporate it into the standard
University, Manisa, Turkey. E-mail: [email protected]
Mehmet Emin Akkaş is with the Department of Project Planning and DEA structure. By using input-output data with determiEvaluation, The Aegean Forestry Research Institute, İzmir, Turkey. nistic, interval and/or fuzzy value, interval DEA model
E-mail: [email protected]
Mustafa Gediklili is with the Trabzon Forest Regional Directorate, has been developed to measure the smallest and the
highest relative efficiency of each decision unit [13, 14].
Turkey. E-mail: [email protected]
Ş. Mümtaz Kanat is with the Muğla Forest Regional Directorate, Thus, by providing interval efficiency or effective interTurkey. E-mail: [email protected]
vals as reference, efficiency value of each decision unit
S. Ümit Portakal is with the Forest Management Controller, İzmir
has been characterized as the best lower limit effectiveForest Regional Directorate, Turkey. E-mail: [email protected]
Manuscript received 20 Dec. 2012; revised 31 May 2013; accepted ness or as the best upper limit effectiveness. As for sequencing and comparison of interval efficiency of the
15 July 2014.
© 2014 TFSA
İ. Şafak et al.: Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data Envelopment Analysis
decision units, Minimax Regret Approach has been used
[13]. On the other hand, DEA is now widely used in the
development of fuzzy models within the scope of
multi-criteria decision making technique such as analytical hierarchy process [14], TOPSIS [15], analytic
network process [16].
DEA applications in forestry were initiated by Rhodes
[17, 18]. The first studies that followed this approach
have focused on the measurement of technical efficiency
of the forestry organizations by means of DEA [18-22].
Later, Lebel and Stuart [23] in determining the contractors who perform logging production works; Zhang [24]
in determining silvicultural activities; Strange [25] in
determining the effectiveness of reserve fields that were
proposed with the intent of the selection of areas of biodiversity and Hof et al. [26] in defining the maximum
potential of the forest and pasture areas, benefited from
DEA technique. Again, the fuzzy DEA models developed by Kao and Liu [27, 28] and Kao [29] were used in
evaluating the effectiveness of forest management units.
These studies have shown that it is possible to carry out
the evaluation of the efficiency by means of DEA; in the
level of forest enterprises/forest sub-districts/forestry
class even in the level of sub-units/activities/staff.
In Turkey, several researches were carried out in order
to determine the efficiency, productivity, success or performance of the forest enterprises by Geray [30], Çağlar
[31], Daşdemir [32, 33], Altunel [34], Şentürk [35] and
so on. It was benefited from standard DEA, Stochastic
Production Frontier Approach [36] and Malmquist Total
Factor Productivity Index [37] in an attempt to evaluate
the efficiency of the Forest Regional Directorates [38]
and forest enterprises [39]. On the other hand Şafak [40]
compared the efficiency level of the forest enterprises
both with standard and fuzzy DEA.
The activities of forestry vary by forest sub-districts.
The changes in the forest structure, ecological differences, the difference in land works, and socio-economic
status of the region etc. factors have prevented to carry
out a one-dimensional of efficiency assessments. So
there are multi dimensional processes in forestry. The
DEA method is multi dimensional and evaluates the efficiency using a large number of input and output variables together.
In this research, different inputs and outputs variables
are used together for the efficiency assessment of forest
sub-districts by fuzzy DEA method.
Efficiency evaluation study had not been carried out at
the level of forest sub-districts in Turkey until this study.
In this research, it is aimed to evaluate efficiency of the
forest sub-districts in the Denizli Forestry Regional Directorate for years 2007 and 2009 using fuzzy DEA.
359
2. Materials and Methods
2.1. Determination of the decision units and variables
Turkey is one of the Mediterranean countries. The
Denizli Regional Forest Directorate is located at western
part of Anatolian peninsula that is typically of Mediterranean climate and vegetation. In this context, 42 of the
forest sub-districts which continue their activities depending on 7 forest enterprises at Denizli Forest Regional Directorate were chosen as decision units.
The protection, development and management of forest are under the responsibility of General Directorate of
Forest, which is one of the connected units of the Ministry of Forestry and Water Affairs. The forest
sub-districts are the smallest units of the General Directorate of Forestry within its provincial organization. The
forest sub-districts have various assignment, authorization and obligations which can be explained under the
headings such as forest resources management, production of forest products, silviculture, forest protection,
construction and maintenance of the forest roads, forest
cadastre and forensic activities. In this research, the efficiency of those forest sub-districts for years of 2007 and
2009 was evaluated using input and output variables as
follows:
Inputs variables:
Total population in the forested land ( x1 ): It expresses
number of forest villager living in forest area of the forest sub-districts (as person).
Total expenditures on silviculture practices ( x 2 ): It
covers all of the cost of activities such as natural regeneration, tending of early saplings (natural growth),
thicket tending, forest rehabilitations, establishment of
plantation forests (reforestations) and tending of early
saplings (plantation forests) (as Turkish lira).
General production expenses ( x3 ): It covers cost of
production for timber harvesting such as cutting, skidding and moving (as Turkish lira).
Total number of employees ( x 4 ): It expresses the total
number of employees in the forest sub-districts (as person).
Annual allowable cut, AAC ( x5 ): It expresses the
amount of the annual yield of forest management planning in the forest sub-districts (as m 3 ).
Forest area ( x6 ): It expresses the amount of forest land
of the forest sub-districts (as hectare).
Output variables:
Number of permissions granted in forested lands ( y1 ):
It expresses the amount of allocated forest land to other
establishments which work outside forest activity (as
number) by the forest sub-districts.
Amount of produced industrial wood ( y 2 ): It ex-
360
presses the amount of industrial wood production of the
forest sub-districts (as m 3 ).
Total amount of the forest roads ( y3 ): It expresses total forest road length in the forest sub-districts (as km).
Amount of the burned area ( y 4 ): It expresses the
amount of annual burned forest area in the forest
sub-districts (as hectare).
Total amount of silvicultural practices ( y 5 ): It covers
all of the silvicultural activities such as natural regeneration, tending of early saplings (natural growth), thinning,
forest rehabilitations, establishment of plantation forests
(reforestations) and tending of early saplings (plantation
forests) (as hectare).
In this article, fuzzy DEA approach based on CCR
model proposed by Wang et al. [20] was used. CCR
model concludes the inputs to be the minimum and also
outputs to be the maximum. Values of the amount of the
burned area ( y 4 ) variable which take place among the
outcomes of the forest sub-districts are required to be the
smallest with regards to the forest resources management.
Therefore, for this variable percentage conversion was
applied. First of all, minimum and maximum values of
the variable to be converted were identified through the
annual data aimed at forest sub-districts. Percentage
conversion was applied on all of the forest sub-districts’
data so that the values of the forest sub-districts which
had the smallest value were 100 and values of the forest
sub-districts which had the largest value were 0. In addition, in DEA analysis the value aimed at variables is
prompted to have a value that is greater than zero. Hence,
the value of the variables which have a value of zero was
considered to be 10-5 in this model.
proach, upper ( a α ) and lower ( a α ) limit values calculated as follows:
a α  a  α(m  a)
(1)
a α  b  α(b  m)
Here, (a) refers to the lower limit value; (b) the upper
limit value and (m) central value of the variable.
Conversion of the constant data into interval values
Total population in the forest land ( x1 ), forest land
( x7 ) and AAC ( x8 ) variables continuously vary at forest
sub-districts. However, those change amounts cannot be
reflected on plans or programs at the same rate. Those
variable values that appear to be constant are converted
into fuzzy data in the form of [42];
a  m  Sh
(2)
b  m  Sh
Here, ( S h ) shows the standard error and is calculated
by S h  S / n . Then, taking the Zimmermann’s [41] “α
cutting set approach” into consideration, fuzzy values are
converted into data that have interval values.
2.3. Installation of the model; determination of the lower
and upper efficiency limit values
During the analysis of activities of the forest
sub-districts in the years 2007-2009 fuzzy DEA approach based on CCR model proposed by Wang et al.
[13] was used. In this context, taking into account five α
level, fuzzy DEA models which give us upper and lower
limit efficiency of the forest sub-districts are developed.
Upper Limit Efficiency Value:
s
Max  Uj 0   ur yUrj 0
(3)
r 1
2.2. Determination of the upper and lower limit values
for the variables
Within fuzzy DEA models, values of the variables
must primarily be converted into interval values. This
process varies depending on whether the values of the
variables are constant or not.
Conversion of the non-constant data into interval values:
The variables such as total number of employees,
general production expenses, total amount of silviculture
practices, total expenditures on silviculture practices,
amount of the burned area, total amount of the forest
roads, number of permissions granted in forested lands
and the amount of industrial wood produced create
non-constant data. First of all, the values of variables in
2007-2009 are defined as lower, central and upper limits
thus fuzzy data are obtained. Then, taking the
Zimmermann’s [41] “α cutting set approach” into consideration, the data that have fuzzy values are converted
into data that have interval values. According to this ap-
m
v x
s
i 1
m
i
u y  v x
r 1
U
r
rj
i 1
i
L
ij 0
L
ij
1
 0, j  1,...,n
ur , vi   , r,i.
Lower Limit Efficiency Value:
s
Max  Lj 0   ur y Lrj 0
(4)
r 1
m
v x
s
i 1
m
U
i
ij 0
u y  v x
r 1
U
r
rj
i 1
i
L
ij
1
 0, j  1,...,n
ur , vi   , r,i.
The legend used above:
 Uj 0 ; Upper limit efficiency value of the forest
sub-districts to be analyzed.
 L ; Lower limit efficiency value of the forest
j0
sub-districts to be analyzed.
n ; The number of the forest sub-districts.
i ; The number of inputs ( i  1, 2,  , m ).
r ; The number of outputs ( r  1, 2,.., s ).
th
th
y j  { y1 j , y 2 j ..., y rj ,..., y sj } , r output value for j forest sub-districts.
th
th
x j  { x1 j , x 2 j ,  , x ij  , x sj } , i input value for j forest
sub-districts.
th
yrj ; Output vector of j forest sub-districts.
th
xij ; Input vector of j forest sub-districts.
vi ; Input weights.
u r ; Output weights.
L; Lower limit values of the forest sub-districts.
U; Upper limit values of the forest sub-districts.
With the model No. (3) presented above upper limit
efficiency values (  Uj 0 ), and also with the model No.(4)
lower limit efficiency values (  Lj 0 ) of the forest
sub-districts are obtained. In this case [ Lj 0 ,  Uj 0 ] , the
best possible relative efficiency range for forest the forest sub-districts is created. In other words, for the five α
level (0, 0.25, 0.50, 0.75, and 1) of the forest
sub-districts, lower and upper limit efficiency values
between 0.00 and 1.00 are calculated. Units whose efficiency values are equal to 1.00 forms the best set of observation as well as efficiency limit and units whose efficiency values are less than 1.00 on the other hand form
relatively inactive decision units.
For each α-level and according to lower and upper
limit values obtained by fuzzy DEA solutions, minimum
values of the maximum efficiency losses of the forest
sub-districts were calculated by Minimax Regret Approach [13].
(5)
Min{Max ( ri }  Min{Max[ Max ( aUj )  aiL ,0]}
i
i
j 1
Here, ri shows the value of efficiency loss calculated
for the forest sub-districts, a Uj within the set of upper
limit efficiency values the highest upper limit efficiency
values of the forest sub-districts to be sequenced and a iL
lower limit efficiency value of the forest sub-districts
whose efficiency loss to be calculated.
3. Results
Lower and upper efficiency values aimed at five α
level of 42 forest sub-districts under Denizli Forest Regional Directorate are given in Table 1. Accordingly, in
terms of the upper limit efficiency values, at all α levels,
the forest sub-districts within Eskere forest enterprise
361
emerged to be effective; however the followings have
been found ineffective;

Değne, Denizli, Sarayköy, Tavas, Eşme and Uşak
Forest Sub-Districts; at all α levels,

Elmaözü Forest Sub-Districts; at α=0.25, 0.50,
0.75 and 1 levels,

Ulubey Forest Sub-Districts; at α=0.50, 0.75 and
1 levels,

Kelekçi Forest Sub-Districts; at α=0.00 and 0.25
levels,

Bozdağ, Çardak and Pamukkale Forest
Sub-Districts; at α=0.00, 0.25 and 0.50 levels,

Çal Forest Sub-Districts; at α=1 level,

Çivril Forest Sub-Districts; at α=0, 0.25, 0.50 and
0.75 levels,

Boyalı Forest Sub-Districts; at α=0 level
Also in terms of the lower limit efficiency values;

at α=0, 0.25, 0.50 and 0.75 levels, except Yatağan
and Yazır, all of the forest sub-districts, and

also at α=1 level, 21 forest sub-districts emerged
to be ineffective.
By using the formula No (5) with lower and upper
limit efficiency values given in Table 1, minimum values
of maximum efficiency loss belonging to the forest
sub-districts were calculated for five α levels and interval efficiency was listed from the best to the worst in
Table 2. Accordingly, at α=0, 0.25, 0.50 and 0.75 levels,
except Yatağan and Yazır, 40 of the forest sub-districts;
at α=1 level on the other hand 21 of the forest
sub-districts had efficiency loss.
4. Discussion
According to the results of the evaluation carried out
with fuzzy DEA, in Table 3 it can be generally seen that
the same sub-districts are usually effective on the basis
of α levels and these sub-districts have less efficiency
loss. Accordingly, five of the forest sub-districts that has
the best efficiency are respectively Yatağan (Acıpayam),
Yazır (Acıpayam), Yenidere (Tavas), Güney (Denizli)
and Konak (Tavas).
In the same way, in Table 4 it can be seen that generally the same sub-districts do not emerge to be effective
on the basis of α levels and these sub-districts have more
efficiency loss. Lower limit efficiency values overlap
with the maximum efficiency loss values in terms of the
five forest sub-districts with the lowest efficiency.
Accordingly, it can be stated that Eşme (Uşak), Çivril
(Çal), Çal (Çal), Sivaslı (Uşak) and Denizli (Denizli)
forest sub-districts are the units with the lowest efficiency according to both maximum efficiency loss values and the lowest lower limit efficiency values. Similarly, results of Eşme (Uşak) and Denizli (Denizli) forest
sub-districts are consistent with each other according to
362
Table 1. In fuzzy DEA solution; upper and lower limit efficiency values of the forest sub-districts.
Forest
enterprises
Forest subdistricts
Acıpayam
Alcı
Bozdağ
Acıpayam
Elmaözü
Kelekçi
Yatağan
Yazır
Baklan
Çal
Çal
Çardak
Çivril
İnceler
Boyalı
Çameli
Çameli
Değne
Göldağı
Buldan
Denizli
Güney
Honaz
Denizli
Kaklık
Kocabaş
Pamukkale
Sarayköy
Çiçekli
Eskere
Eskere
Eşenler
Karacaören
Yelkencidağ
Kale
Konak
Tavas
Köprübaşı
Tavas
Yenidere
Banaz
Çamsu
Çatak
Eşme
Uşak
Sivaslı
Uşak
Ulubey
Güre
The number of ineffective
sub-districts
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
α=0.00
α=0.25
α=0.50
α=0.75
α=1.00
Lower
Upper
Lower
Upper
Lower
Upper
Lower
Upper
Lower
Upper
0.7141
0.5801
0.6927
0.6941
0.6204
1
1
0.6537
0.4568
0.6120
0.3644
0.7368
0.6696
0.6553
0.7093
0.8399
0.9179
0.5139
0.9588
0.6879
0.7819
0.9292
0.7749
0.7581
0.8295
0.8833
0.9001
0.7978
0.5219
0.7214
0.9274
0.7922
0.6655
0.9961
0.8141
0.8700
0.8534
0.3317
0.4825
0.6168
0.5689
0.6189
1
1
0.8887
1
0.8749
1
1
1
1
0.8732
0.5184
1
0.9592
1
0.9598
1
1
0.6431
1
1
1
1
0.9683
0.9499
1
1
1
1
1
1
1
1
0.9461
1
1
1
1
0.6303
1
0.8976
1
1
0.7522
0.6097
0.7406
0.7037
0.6776
1
1
0.6976
0.5308
0.6555
0.3885
0.7659
0.7289
0.7757
0.7267
0.8598
0.9206
0.5410
0.9622
0.7252
0.7896
0.9476
0.7978
0.7909
0.8524
0.8848
0.9115
0.7995
0.5926
0.7687
0.9494
0.7968
0.6959
0.9971
0.8679
0.8769
0.8561
0.3321
0.5101
0.6201
0.5723
0.7240
1
1
0.9245
0.9689
0.9294
1
1
1
1
0.8884
0.6067
1
1
1
0.9336
1
1
0.6769
1
1
1
1
0.9831
0.9571
1
1
1
1
1
1
1
1
0.9535
1
1
1
1
0.6393
1
0.8909
1
1
0.7903
0.6658
0.7980
0.7134
0.7636
1
1
0.7578
0.6267
0.7429
0.4687
0.8109
0.8021
0.8484
0.7533
0.9035
0.9234
0.5952
0.9675
0.7855
0.8078
0.9649
0.8209
0.8244
0.8643
0.8863
0.9232
0.8086
0.6755
0.8176
0.9683
0.8142
0.7349
0.9981
0.8991
0.8902
0.8596
0.3339
0.6200
0.6246
0.5894
0.7998
1
1
0.9630
0.9441
1
1
1
1
1
0.9346
0.7489
1
1
1
0.9352
1
1
0.7159
1
1
1
1
0.9961
0.9646
1
1
1
1
1
1
1
1
0.9587
1
1
1
1
0.7404
1
0.8681
0.8772
1
0.8380
0.7603
0.8597
0.7379
0.8475
1
1
0.8484
0.7827
0.8684
0.7230
0.8910
0.8583
0.9264
0.8062
0.9503
0.9285
0.6966
0.9812
0.8628
0.8531
0.9823
0.8440
0.8636
0.8783
0.9442
0.9501
0.8399
0.8112
0.8833
0.9850
0.8702
0.7925
0.9990
0.9427
0.9411
0.9119
0.4941
0.7711
0.6744
0.6989
0.8903
1
1
1
0.9502
1
1
1
1
1
1
0.9140
1
1
1
0.9471
1
1
0.7654
1
1
1
1
1
0.9725
1
1
1
1
1
1
1
1
0.9566
1
1
1
1
0.8530
1
0.8512
0.8345
1
0.9951
0.8930
0.9661
0.7703
0.9600
1
1
1
0.9640
1
1
1
0.9441
1
0.9187
1
0.9584
0.8375
1
0.9424
0.9450
1
0.8655
0.9157
0.9888
1
1
0.9160
1
1
1
0.9830
0.9155
1
1
1
1
0.8198
1
0.7643
0.9079
1
1
1
1
0.9491
1
1
1
1
0.9640
1
1
1
1
1
0.9282
1
1
0.8597
1
1
1
1
1
0.9835
1
1
1
1
1
1
1
1
0.9297
1
1
1
1
0.8198
1
0.8161
0.9079
1
40
12
40
12
40
12
40
9
21
9
both maximum efficiency loss values and the lowest upper limit efficiency values. Accordingly also, Eşme
(Uşak), Denizli (Denizli), Çivril (Çal), Ulubey (Uşak)
and Uşak (Uşak) forest sub-districts can be concluded to
be the units with the lowest efficiency.
When taking the earlier studies conducted by DEA
into consideration, Denizli Forest Regional Directorate
was not found to be effective on the efficiency assessment [38] carried out for the year 2002 on the basis of 27
of the Forest Regional Directorates in Turkey and its
efficiency value was calculated as 0,5673. Also through
the efficiency rating conducted on the basis of 26 of the
forest enterprises in Aegean Region [40], while Çameli,
Eskere and Tavas forest enterprises of Denizli Forest
Regional Directorate emerged to be efficient, Uşak,
Denizli, Çal and Acıpayam forest enterprises took place
among the forest sub-districts with the most ineffectiveness.
363
Table 2. Minimum values of the efficiency loss (EL) of the forest sub-districts on the basis of α level.
No
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
α=0.00
Sub-districts
Yatağan
Yazır
Yenidere
Güney
Kocabaş
Konak
Buldan
Eşenler
Eskere
Çamsu
Çatak
Göldağı
Çiçekli
Banaz
Karacaören
Köprübaşı
Kaklık
Pamukkale
Sarayköy
İnceler
Kale
Acıpayam
Değne
Elmaözü
Bozdağ
Honaz
Boyalı
Tavas
Çameli
Baklan
Kelekçi
Güre
Uşak
Çardak
Alcı
Ulubey
Yelkenc.
Denizli
Sivaslı
Çal
Çivril
Eşme
EL
0
0
0.0039
0.0412
0.0708
0.0726
0.0821
0.0999
0.1167
0.1300
0.1466
0.1601
0.1705
0.1859
0.2022
0.2078
0.2181
0.2251
0.2419
0.2632
0.2786
0.2859
0.2907
0.3059
0.3073
0.3121
0.3304
0.3345
0.3447
0.3463
0.3796
0.3811
0.3832
0.3880
0.4199
0.4311
0.4781
0.4861
0.5175
0.5432
0.6356
0.6683
No
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
α=0.25
Sub-districts
Yatağan
Yazır
Yenidere
Güney
Konak
Kocabaş
Buldan
Eşenler
Eskere
Çamsu
Banaz
Göldağı
Çatak
Çiçekli
Karacaören
Pamukkale
Köprübaşı
Sarayköy
Kaklık
Çameli
Kale
İnceler
Acıpayam
Bozdağ
Boyalı
Değne
Honaz
Güre
Elmaözü
Baklan
Tavas
Kelekçi
Çardak
Uşak
Alcı
Yelkenc.
Ulubey
Denizli
Çal
Sivaslı
Çivril
Eşme
EL
0
0
0.0029
0.0378
0.0506
0.0524
0.0794
0.0885
0.1152
0.1231
0.1321
0.1402
0.1439
0.1476
0.2005
0.2022
0.2032
0.2091
0.2104
0.2243
0.2313
0.2341
0.2478
0.2594
0.2711
0.2733
0.2748
0.2760
0.2963
0.3024
0.3041
0.3224
0.3445
0.3799
0.3903
0.4074
0.4277
0.4590
0.4692
0.4899
0.6115
0.6679
No
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
α=0.50
Sub-districts
Yatağan
Yazır
Yenidere
Konak
Güney
Kocabaş
Buldan
Eşenler
Göldağı
Banaz
Çamsu
Eskere
Çiçekli
Çatak
Çameli
Sarayköy
Pamukkale
Kale
Köprübaşı
İnceler
Karacaören
Kaklık
Boyalı
Güre
Bozdağ
Acıpayam
Honaz
Kelekçi
Baklan
Değne
Çardak
Tavas
Elmaözü
Yelkenc.
Alcı
Çal
Uşak
Sivaslı
Denizli
Ulubey
Çivril
Eşme
In this article on the other hand, efficiency comparison
was made at the level of the forest sub-districts. Accordingly, all forest sub-districts of Çameli, Eskere and Tavas forest enterprises which were effective at Şafak’s [40]
study as well as Eşme, Çivril, Çal, Sivaslı and Denizli
forest sub-districts of Uşak, Denizli and Çal forest enterprises which had lowest efficiency at Şafak’s [40]
study took place among the five of the forest
sub-districts with the lowest efficiency. Again, Güney,
Yatağan and Yazır forest sub-districts of Denizli and
Acıpayam forest enterprises which had the lowest effi-
EL
0
0
0.0019
0.0317
0.0325
0.0351
0.0766
0.0768
0.0965
0.1009
0.1098
0.1137
0.1357
0.1404
0.1516
0.1756
0.1791
0.1824
0.1858
0.1891
0.1914
0.1922
0.1979
0.2002
0.2020
0.2097
0.2145
0.2364
0.2422
0.2467
0.2571
0.2651
0.2866
0.3245
0.3342
0.3733
0.3754
0.3800
0.4048
0.4106
0.5313
0.6661
No
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
α=0.75
Sub-districts
Yatağan
Yazır
Yenidere
Konak
Kocabaş
Güney
Göldağı
Eşenler
Eskere
Banaz
Çamsu
Buldan
Çameli
Çatak
İnceler
Güre
Kale
Çiçekli
Köprübaşı
Çardak
Sarayköy
Honaz
Bozdağ
Boyalı
Kaklık
Baklan
Kelekçi
Pamukkale
Karacaören
Acıpayam
Yelkenc.
Değne
Tavas
Çal
Sivaslı
Alcı
Elmaözü
Çivril
Ulubey
Denizli
Uşak
Eşme
EL
0
0
0.0010
0.0150
0.0177
0.0188
0.0497
0.0499
0.0558
0.0573
0.0589
0.0715
0.0736
0.0881
0.1090
0.1097
0.1167
0.1217
0.1298
0.1316
0.1364
0.1372
0.1403
0.1417
0.1469
0.1516
0.1525
0.1560
0.1601
0.1620
0.1888
0.1938
0.2075
0.2173
0.2289
0.2397
0.2621
0.2770
0.3011
0.3034
0.3256
0.5059
No
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
α=1.00
Sub-districts
Güre
Sivaslı
Çatak
Çamsu
Banaz
Yenidere
Konak
Kale
Yelkenc.
Eşenler
Eskere
Kocabaş
Güney
Göldağı
Çameli
İnceler
Çivril
Çardak
Baklan
Yazır
Yatağan
Acıpayam
Çiçekli
Köprübaşı
Bozdağ
Çal
Kelekçi
Buldan
Kaklık
Boyalı
Honaz
Değne
Karacaören
Sarayköy
Tavas
Ulubey
Alcı
Pamukkale
Denizli
Eşme
Elmaözü
Uşak
EL
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.0049
0.0112
0.0170
0.0339
0.0360
0.0400
0.0416
0.0550
0.0559
0.0576
0.0813
0.0840
0.0843
0.0845
0.0921
0.1070
0.1345
0.1625
0.1802
0.2297
0.2357
ciency at Şafak’s [40] study as well as Yenidere and
Konak forest sub-districts of Tavas forest enterprises
which was also effective at Şafak’s [40] study took place
among the top five forest sub-districts.
Accordingly, the forest sub-districts which have the
best (or the worst) efficiency can be found at the forest
enterprises which have the worst (or the best) efficiency.
Therefore, any forest enterprises being effective (or ineffective) does not necessarily mean that all of the forest
sub-districts connected to the relevant forest enterprises
are effective (ineffective).
364
Table 3. Five of the forest sub-districts with the highest values in terms of maximum efficiency loss and lower limit efficiency
values.
α=0.00
Yatağan
Yazır
Yenidere
Güney
Kocabaş
α=0.25
α=0.50
α=0.75
According to the highest lower limit efficiency values*
1
1
0.9961
0.9588
0.9292
Yatağan
1
Yatağan
1
Yatağan
1
Yazır
1
Yazır
1
Yazır
1
Yenidere
0.9971
Yenidere
0.9981
Yenidere
0.9990
Güney
0.9622
Konak
0.9683
Konak
0.9850
Konak
0.9494
Güney
0.9675
Kocabaş
0.9823
According to the values that are the best of the maximum efficiency loss*
α=1.00
Yatağan
Yazır
Yenidere
Güney
Konak
1
1
1
1
1
Yatağan
0
Yatağan
0
Yatağan
0
Yatağan
0
Yatağan
0
Yazır
0
Yazır
0
Yazır
0
Yazır
0
Yazır
0
Yenidere
0.0039
Yenidere
0.0029
Yenidere
0.0019
Yenidere
0.0010
Yenidere
0
Güney
0.0412
Güney
0.0378
Konak
0.0317
Konak
0.0150
Güney
0
Kocabaş
0.0708
Konak
0.0506
Güney
0.0325
Kocabaş
0.0177
Konak
0
*
At α=1 level, lower limit efficiency value of 21 of the forest sub-districts are 1. Therefore, only the forest sub-districts with the highest upper limit values at
the other α levels are given in α=1 level column of the Table.
Table 4. Five of the forest sub-districts with lowest values in terms of maximum efficiency loss and lower and upper limit efficiency values.
α=0.00
α=0.25
Eşme
Çivril
Çal
Sivaslı
Denizli
0.3317
0.3644
0.4568
0.4825
0.5139
Eşme
Çivril
Sivaslı
Çal
Denizli
Çivril
Eşme
Denizli
Çardak
Kelekçi
0.5184
0.6303
0.6431
0.8732
0.8749
Çivril
Eşme
Denizli
Çardak
Uşak
Eşme
Çivril
Çal
Sivaslı
Denizli
0.6683
0.6356
0.5432
0.5175
0.4861
Eşme
Çivril
Sivaslı
Çal
Denizli
α=0.50
α=0.75
According to the lowest lower limit efficiency values
0.3321
Eşme
0.3339
Eşme
0.3885
Çivril
0.4687
Uşak
0.5101
Ulubey
0.5894
Denizli
0.5308
Denizli
0.5952
Ulubey
0.5410
Sivaslı
0.6200
Çivril
According to the lowest upperlimit efficiency values
0.6067
Denizli
0.7159
Denizli
0.6393
Eşme
0.7404
Ulubey
0.6769
Çivril
0.7489
Uşak
0.8884
Uşak
0.8681
Eşme
0.8909
Ulubey
0.8772
Çivril
According to the values whose maximum efficiency loss are the worst
0.6679
Eşme
0.6661
Eşme
0.6115
Çivril
0.5313
Uşak
0.4899
Ulubey
0.4106
Denizli
0.4692
Denizli
0.4048
Ulubey
0.4590
Sivaslı
0.3800
Çivril
5. Conclusion
A large number of activities are executed in the forest
sub-districts. The intensity of these activities are differentiated according to the changes in the forest structure,
ecological differences, the difference in land works,
socio-economic status of the region etc. Therefore, in the
evaluation of efficiency of forestry activities need to use
multi-dimensional models as DEA.
DEA is widely used in measuring the relative efficiency of decision units belong to the large number of
inputs and outputs variables. In recent years, DEA studies have been focused on how to convert data with fuzzy
value into data with precise value and how to incorporate
it into the standard DEA structure. For this purpose,
many research projects on the fuzzy DEA models have
been conducted to find newer and better ways.
α=1.00
0.4941
0.6744
0.6966
0.6989
0.7230
Uşak
Elmaözü
Eşme
Denizli
Pamukkale
0.7643
0.7703
0.8198
0.8375
0.8655
0.7654
0.8345
0.8512
0.8530
0.9140
Uşak
Eşme
Denizli
Ulubey
Değne
0.8161
0.8198
0.8597
0.9079
0.9282
0.5059
0.3256
0.3034
0.3011
0.2770
Uşak
Elmaözü
Eşme
Denizli
Pamukkale
0.2357
0.2297
0.1802
0.1625
0.1345
In this article, efficiency comparison was made at the
level of the forest sub-districts in the Denizli Forest Regional Directorate by Fuzzy DEA. According to the
results of the evaluation carried out with fuzzy DEA,
five of the forest sub-districts that have the best efficiency are the same on the basis of α level. In the same
way, generally the same sub-districts do not emerge to
be effective on the basis of α level. Accordingly, fuzzy
DEA method could be used to determine the efficiency
level of forest sub-districts in Turkey.
Fuzzy DEA applications in forestry were made mostly
on the levels of technical efficiency. But, as the classical
DEA applications, next period, fuzzy DEA applications
will be made based on forestry targets, strategies or activities. Accordingly, some topics are shown below as,
 Evaluations of the efficiency of soil, flora and fauna
with regard to the forest areas.
Evaluations of the efficiency of issues that are fire,
erosion, pollution etc.
 Evaluations of efficiency of alternative management
scenarios in terms of the forest functions.
 Evaluations of the efficiency of quantity and quality of
water produced in forest.
 Evaluations of the efficiency of afforestation and
nursery activities.
As a result, it is possible to measure the technical efficiency of the forest sub-districts which are public institutions and exist within the structure of any forest enterprises using measurable/observable data and to evaluate
them through fuzzy DEA technique. Thus, the opportunity of comparing those units undertaking the same activities or alike with each other, evaluating and planning
for subsequent periods can be given. On the other hand,
take into account that each of the forest sub-districts
connected to the same forest enterprises have distinctive
conditions and that input and output resources differ,
efficiency ratings in forestry should be performed individually for each hierarchical structure.

Acknowledgement
In this article, intermediate results, regarding to
Denizli Forest Regional Directorate, of the TÜBİTAK
(Scientific and Technological Research Council of Turkey) project called “Efficiency Determination of the
Forest Sub-Districts by Using Fuzzy Data Envelopment
Analysis (Denizli, İzmir and Muğla Forest Regional Directorates Case Study)” and numbered 110O126, were
used. We would like to thank TÜBİTAK for supporting
this project.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
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approach,” African Journal of Agricultural Research, vol. 6, no. 28, pp. 6189-6196, 2011.
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Ismail Şafak graduated from department of Forest engineering in Karadeniz
Technical University, Turkey as a forest
engineer. He received his Ph.D. degree
in Department of Business Administration, Institute of Social Science, Celal
Bayar University. He works with department of forest management and
economics research at the Aegean Forestry Research Institute. His major field of research includes
forest economics, management of forest enterprises, wildlife
management and economics, and data envelopment analysis.
Altay Uğur Gül graduated from department of Forest engineering in
Karadeniz Technical University, Turkey
as a forest engineer. He received his
Ph.D. degree in Department of Forest
Management, Institute of Science, in
Karadeniz Technical University. He
works as a professor at the School of
Tobacco Expertise, Celal Bayar University. His major field of research includes forest management,
data envelopment analysis, linear programming, and goal programming.
Mehmet Emin Akkaş graduated from
department of Forest engineering in
as a Forest Industry Engineer. He works
with department of project planning and
evaluation, the Aegean Forestry
Research Institute. His areas of expertise
are statistics.
Mustafa Gediklili graduated from
as a Forest Engineer. He works as a
director of Trabzon Forest Regional
Directorate. His areas of expertise are
forest administration and management.
Ş. Mümtaz Kanat graduated from
as a Forest Engineer. He works as an
inspector at Mugla Forest Regional
Directorate. His areas of expertise are
forest administration and management.
367
S. Ümit Portakal graduated from
as a Forest Engineer. He works as an
forest management controller at Izmir
Forest Regional Directorate. His areas of
expertise are forest management and
planning.

Efficiency Determination of the Forest Sub

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