Assessment of combating-desertification strategies using the linear assignment method

Nowadays desertification, as a global problem, affects many countries in the world, especially developing countries like Iran. With respect to increasing importance of desertification and its complexity, the necessity of attention to the optimal combating-desertification alternatives is essential. Selecting appropriate strategies according to all effective criteria to combat the desertification process can be useful in rehabilitating degraded lands and avoiding degradation in vulnerable fields. This study provides systematic and optimal strategies of combating desertification by use of a group decision-making model. To this end, the preferences of indexes were obtained through using the Delphi model, within the framework of multi-attribute decision making (MADM). Then, priorities of strategies were evaluated by using linear assignment (LA) method. According to the results, the strategies to prevent improper change of land use (A18), development and reclamation of plant cover (A23), and control overcharging of groundwater resources (A31) were identified as the most important strategies for combating desertification in this study area. Therefore, it is suggested that the aforementioned ranking results be considered in projects which control and reduce the effects of desertification and rehabilitate degraded lands.

1 solutions among the several solutions based on different desertification criterion. Therefore, in order to achieve this goal in 2 the context of decision-making models and linear assignment (LA) method were used to rank combat to desertification 3 alternatives.

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Managing desert ecosystems is a collection of various managements to optimize control of desertification phenomenon and 5 minimize the loss of economy, society and environment. Making decision in management of desert areas is a complex issue 6 due to various indexes and various criterions for decision in such areas. There are several ways to achieve a specific purpose 7 since each has different preferences for the different issues of environmental, social, political and economical organization.

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These requirements lead to the use of Multi Attribute Decision Making (MADM) which its purpose is to choose the best 9 answer among the different solutions. The purpose of this study while considering the limitation of inputs is to assess 10 desertification strategies to achieve the optimal strategies in the framework of sustainable management of desert area. To 11 achieve this goal with framework of MADM, using Linear Assignment (LA) were considered to rank combating 12 desertification strategies which is a kind of Concordance Methods. This method having a simple algorithm has this ability to 13 engage simultaneously a large number of quantitative and qualitative criteria in the decision process. In different intervals of 14 time and place, it is also capable to change the input data and provide new assessment according to this change. Therefore 15 comparative studies are easy to do (Asgharpour, 1999).

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According to using descriptive data instead of principal data in this method, so it is easy to understand and has been used in 17 various fields of science (Bernardo and Blin, 1977). Some of these studies including assessment of environmental

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Programming of robots (Ji et al, 1992), Programming for dispatching helicopter in emergency missions (Celi, 2007) And so 26 on. In order to select the optimal strategies for providing an integrated plan to control erosion and desertification, Grau used 27 three decision models in his research; ELECTRE, AHP and PROMETHEE (Grau et al, 2010). The results indicate the high 28 efficiency of these models to provide optimal strategy of combating desertification, despite complex methods which are used 29 in each model; the results were largely the same. Sadeghi ravesh prioritize the strategies in Khezr Abad region, by using the

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The climate of this region is cold and arid based on Amberje climate classification method. About 12,930 ha (16.5%) of the 5 region are hilly and the sand dune area (sandy desert with inselberges) which shows absolute typical condition of 6 desertification in the study area, hence the following effective solution and optimum combating desertification alternatives

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Although the weight vector of indexes have been obtained through expert opinion and Delphi model: Selecting criteria and alternatives can be done individually according to expert experience, resources, and field studies or 21 using Delphi method, distributed a structured questionnaire among experts familiar with the study area. The experts were 22 asked to rate effective criteria and alternatives between 0 and 9. Finally, mean values were calculated. In this case, if the 23 mean value was less than 7 ( X <7), related criterion and alternative was removed and if the mean value was more or equal to  in order to achieve Local Priority, the structured questionnaire was designed based on literature and the nine-point Sa'aty 1 scale, from 1(least important) to 9 (most important) were used to measure the relative importance of criteria and priority of 2 combating desertification alternatives (Table 1).

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The questionnaire was distributed among experts familiar with the study area. In continuation, using geometric mean and 4 assumption of uniform expert's opinion, pairwise comparisons of each expert (Table 2) were composed according to Eq. 1; 5 and pairwise comparisons were formed regarding to group.   Relatively high Strongly-Very strongly 7 High Very strongly 8 Very high Very strongly-Extremely 9 Excellent Extremely 1/2, 1/3,1/4, …., 1/9 Mutual Values

Ranking each option for each index 1
After forming the decision making matrix, attempted to rank the alternatives (Ai) for each criteria (Ci) with respect to the 2 desirability of increasing or decreasing and with n×m matrix framework (Table 6).
3 Table 6. Matrix ranking of each option against each index   Matrix elements include the total weight of indexes which alternative i has rank k. Gamma matrix is a assignment matrix, so 10 the optimal solution can be obtained by any kind of assignment methods such as shipping method, Hungarian method, grid 11 method and one and zero linear programming method. The most common method for solving the linear assignment is      Therefore, the Delphi method was used to identify important and preferred criteria and alternatives regarding to group, and 10 to establish hierarchical structure (Saaty, 1995). For this aim, the structured questionnaire in two parts including criteria and 11 alternatives was distributed among experts familiar with the study area. In continuation, arithmetical mean was used to 12 calculate the mean of obtained results. Finally, mean values were calculated. In this case, if the mean value was less than 7 ( 13 X <7), related criterion and alternative was removed and if the mean value was more or equal to 7 ( X ≥7) related criterion 14 and alternative was used to design hierarchical decision structure (Fig. 1).

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In order to estimate the relative weight or priority of criteria and alternatives, pairwise comparisons questionnaire was 17 prepared and distributed among the experts. In continuation, the group pair wise comparisons matrix of criteria importance to 18 goal and alternatives priority to each criterion was formed by obtaining expert opinions and combining their ideas by 19 geometric mean. To prevent the prolongation of the Word, just matrix of criteria importance is presented (Table 7), and 20 alternatives priority to each criteria calculated by this method.  Considering these graphs, it is observed that the alternatives are different based on each criterion. Therefore, decision 1 making matrix of optimal combating desertification alternatives according to the group (Table 9) was formed to select final 2 alternatives and classification of their priorities, in general framework of MADM (Table 3).
3 Table 9. Decision matrix of optimal combating desertification alternatives according to group

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After forming the decision making matrix, attempted to rank the alternatives (Ai) for each criteria (Ci) in a 5×5 matrix which 6 the rows represent rank and columns represent the index (Table10). Decision Matrix of combating desertification alternatives 7 has increasing desirability, it means if the allocate number to each alternative priority associated with each criterion be more,

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then it represents the more priority of this alternative to achieve the goal, Therefore, in any criterion which gain the highest 9 priority is the optimal alternative.

Forming γ 5×5 matrix according to criteria weights (W)
12 At this stage a 5 × 5 gamma matrix is formed, Matrix was estimated by sum of indexes weights which the alternative of i has 13 rank of k. As mentioned, the weight of each index was calculated by survey of experts and based on Delphi method (Table   14   11).

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Gamma matrix is an assignment matrix, and as mentioned the optimal answer can be obtained by any of assignment 16 methods. The most common method for solving the linear assignment method is linear programming.  3 matrix was formed (Table 11). Since the decision variable contain zero and one values, so the output of this program is 4 provided only based on the number 1 in Table 12 then according to this table, scoring table of options was formed (Table   5 13).
6    1 criteria have qualitative or unknown structure that cannot be accurately measured. In such case, fuzzy numbers can be used 2 in order to achieve evaluation matrix. Prioritization method can be developed using fuzzy method. Another disadvantage of 3 this method is: regardless the amount of data and just considering the data ranks, so large amounts of data is lost and 4 achieving results with high accuracy is not possible (Mohammadi, 2011). Therefore try to do not use rating models as  desertification. Although the government has performed many projects to combat desertification in recent years, it seems that 22 they are not adequate due to the country's extensive arid regions. The problem needs more attention in addition to effective 23 cooperation in the national as well as international scene over the long-term.

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In this research, the linear assignment method methods were used to give optimum alternatives in de-desertification. In

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-Taking serious spatial planning and estimation of ecological potential at national, regional and local levels and adapting the

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-Prevent degradation of Haloxylon habitats and effort taken towards their rehabilitation.

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-Consider the balance of livestock and pasture capacity.

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-Considering the suitability of livestock to the pastures. Try to reduce the number of goats in poor pasture because this 7 animal is considered as an escalation potential factor in degrading rangelands.

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-Avoid grazing off-season in desert rangelands (early and late grazing) because of degradation of poor vegetation.

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-According to protect rangelands and support ranchers, used to produce and import forage increase the sustainable economic 10 potential of ranches to stop them from residue grazing of farms and gardens and cutting brush which they do for night and 11 winter livestock grazing, so acceleration of the degradation is prevented.

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Finally, it is recommended to combating desertification schemes in the study area based on these alternatives is to prevent 13 loss of limited investments and increase the efficiency of control, reclamation and construction plans. The results of this 14 study will allow desert managers to apply limited investment and facilities in efficient ways, which are assigned to control 15 the process of desertification. So either we can achieve better results or avoid wasting the national investments.

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The results of this research can be used in future investments aiming at obtaining a sustainable development, so that the 17 marginal ecosystems and investments in arid and semi-arid region will be protected. On the other hand, it will help the