Efficiency Determination of the Forest Sub
Transkript
Efficiency Determination of the Forest Sub
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: isafak35@hotmail.com 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: ugurgul1@hotmail.com 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: emin_akkas@yahoo.com 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: mustafagediklili@hotmail.com Ş. Mümtaz Kanat is with the Muğla Forest Regional Directorate, Thus, by providing interval efficiency or effective interTurkey. E-mail: mumtazkanat@hotmail.com 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: umitp@hotmail.com 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 International Journal of Fuzzy Systems, Vol. 16, No. 3, September 2014 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. İ. Şafak et al.: Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data Envelopment Analysis 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 International Journal of Fuzzy Systems, Vol. 16, No. 3, September 2014 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. İ. Şafak et al.: Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data Envelopment Analysis 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 International Journal of Fuzzy Systems, Vol. 16, No. 3, September 2014 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. İ. Şafak et al.: Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data Envelopment Analysis 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. 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Güneş, “Fuzzy Data Envelopment Analysis,” Ankara University, Graduate School of Natural and Applied Sciences, Department of Statistics, Master Thesis, Turkey, 2006. İ. Şafak et al.: Efficiency Determination of the Forest Sub-Districts by Using Fuzzy Data Envelopment Analysis 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 Karadeniz Technical University, Turkey 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 department of Forest engineering in Karadeniz Technical University, Turkey 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 department of Forest engineering in Karadeniz Technical University, Turkey 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 department of Forest engineering in Karadeniz Technical University, Turkey 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.