Application of Fuzzy Multi-objective Decision Making Model for Adapted Cropping Pattern to climate change:A Case Study of Pishin River Basin of Iran

: Water management denotes one of the most critical problems that face the national interests in the current and near future, especially in the middle east, where, according to UNESCO, the main interstate conflicts over water occur/will occur in that region. Given that agricultural irrigation water accounts for 80% consumption of the world’s water resources, better agricultural systems management can play a critical role in the peaceful resolution of such crisis. Agricultural sector of Iran on the basis of special climate and geographic position poses many challenges and problems. Among these challenges, crop selection and water management are very important. That is, to decide on the proper set of crops to be cultivated and a proper irrigation scheme. So farmers must balance conflicting objectives when planning production. Conflicts may embrace economic, environmental, cultural, social, technical, and aesthetic objectives. Selecting the best combination of management uses from numerous objectives is difficult. Fuzzy Multi-Objective Decision making (FMCD) Models provides a systematic technique for selecting alternatives that best satisfy the farmer’s objectives when objectives or restrictions are not clear. Fuzzy multiple criteria decision making models generally rely on the aggregation of the objectives to form a decision function and it allows trade-off among the objectives, and has been shown to be suitable to model decision making behavior. Such decisions are made to realize a certain objectives that typically include the maximization of net profit and the minimization of required investment, minimization of water consumption. So in this research an adapted crop pattern was determined by using Fuzzy Multi-Objective decision making model.

demand for food and agricultural products. However, water demand has increased dramatically as well. Given the limited water resources, water demands pertaining to domestic, industrial, and agricultural use put an extreme burden on the existing water supply systems. In this taxing situation, the water quantity of reservoir must be managed. Ideal water resource management involves many different components, including balancing water distribution, ensuring efficient integrated management, minimizing costs, and protecting the ecosystem.( Chen, C. F. Chen, Y. C., and Yang, J. L. 2008, p. 4) The task of reservoir operation and planning remains incomplete without ensuring the beneficial use of obtained releases for irrigation. It requires that cropping pattern must be readjusted with respect to possible releases available. Therefore, the second step, following reservoir management, is the problem of irrigation water management. Essentially, three decisions are required in irrigation water management, namely optimal crop selection, optimal land allocation under different selected crops, and optimal amount of water to be allocated to each crop. Optimization techniques provide a powerful tool for analysis of problems that are formulated with single, quantifiable objectives.( Gupta, A. P., Harboe, R., 2000, p. 1) To support farmers and optimally allocate scarce resources, decision support models are developed. Decision support models are including mainly large band of consequences of cropping plan decisions at the farm and higher levels, the valuation or designing of cropping plans that based on the concepts of the cropping pattern. The assessment and designing of cropping plans using models are driven by many different motivations. Cropping plan selection models are typically used to support farmers, policy maker and other shareholders in defining strategies to allocate scarce and competing resources more efficiently. Cropping plan selection models are used in research project aiming at different outcomes and are differently used within these projects. (Matthews, 2011, p. 3) In 1998, Aubry et al. state that Cropping plan decisions are the main land-use decisions in farming systems and it have strong impacts on resource use efficiency and on environmental processes at both farm and landscape scales. These decisions mostly occur at the farm level and are consequently part of the global technical management of farm production. The modeling of cropping plan selection has been treated using a variety of approaches based on different objectives and they are often selected based on a single monetary criterion, i.e. profit maximization (Audsley, 1993;Itoh et al., 2003;Leroy and Jacquin, 1991). Single criterion models mainly differ from multi-criteria ones in the way in which the cropping plan decision problem is formalized (annual or rotational) and in the set of constraints that are considered for restricting profit maximization. Although it is commonly acknowledged that cropping systems must generate incomes for farmers, some researchers (Bartolini et al., 2007;Foltz et al., 1995;Gupta, et.al., 2000;Piech and Rehman, 1993;Stone et al., 1992) point out the restrictions of an approach that focuses completely on return maximization. They argue that decision making problems like crop area planning contain consideration of multiple, conflicting and non-commensurable criteria. Objectives that influence the selection of a cropping plan have to reflect the different goals, perspectives and values of the decision-makers. These are called and formulated in multiple-criteria decision making models (MCDM. Besides, growing environmental concerns have led researchers to explicitly target objectives other than profitability (DeVoilet al., 2006;Dogliotti et al., 2005;Foltz et al., 1995;Rehman and Romero, 1993). Further, in order to meet various requirements, multiple criteria are inevitably required in programming, leading to multiple criteria decision making (MCD). However, the criteria always conflict with each other. For example, minimizing investment levels while also maximization the net benefits or maximization of labor employment associated with maximize irrigation of cultivated lands is a classic example of conflicting objectives in water management.

International Journal of Academic Research in Economics and Management Sciences
March 2014, Vol. 3, No. 2 ISSN: 2226-3624 Multiple optimization programming is aimed at achieving a compromised optimum among objectives but will not yield an absolute decision. While pursuing adequate management, some nuisance characteristics often exist, such as variability, uncertainty, and nonlinear characteristics; thereby hindering the complete development of a system. To overcome these difficulties, systematic and reliable programming is required (C.F. Chen, et al., 2008). In 1992, Stone et al., and Nevo et al., 1994 have argued that using quantitative and deterministic methods alone is not enough to achieve satisfactory cropping plans due to the nature of the information that is required, as such information is often incomplete, qualitative and uncertain. However, uncertainty due to the random character of natural processes of the real-world decision making problems to result in it can not to be defined precisely in mathematical terms (because of fuzziness). Further, it can not be dealt with quantitatively by various developed techniques and tools provided by probability, decision, control and information theories. These rules are based on expert knowledge and are "quantified" using fuzzy logic techniques for logical conclusion or Bayesian theory to deal with uncertain processes. Klir and Yuan, (1995) state that the fuzziness behavior of a decision making problem is characterized by a system of IF-THEN rules which can be considered as a set fuzzy. While associating fuzzy function with logical implication rule, there appear two problems (i) how this function can be represented, and (ii) how it can be used in calculations. Since a fuzzy function is a fuzzy relation, therefore, it is a common practice to represent a system of fuzzy IF-THEN rules as a fuzzy relation so that the required calculations can be performed using the compositional rule of inference.
In other developmental study (Bergez et al., 2010), designed crop management system by simulation. They followed four-step loop (GSEC): (i) generation; (ii) simulation; (iii) evolution; (iv) comparison and choice. In 2009, Sharma and Jana used fuzzy goal programming based GA approach to nutrient management for rice crop planning. They present a tolerance based fuzzy goal programming (FGP) and a FGP based GA model for nutrient management decision making for rice crop planning in India. They included fuzzy goals such as fertilizer cost and rice yield in the decision-making process Bellman and Zadeh (1970) argued that water resources management takes place in an environment in which the basic input information, goals, constraints, and consequences of possible actions are not known precisely. Therefore, water resource managers and modelers are bound to deal with imprecision mostly due to insufficient data and imperfect knowledge which should not be equated with randomness and the consequent uncertainty. Hence, it is more realistic to consider imprecise model constraint and goals. Fuzzy goals and/or fuzzy constraints are regarded as fuzzy criteria.

Fuzzy set theory:
The fuzzy set theory was introduced by Zadeh (1965) It was oriented to the rationality of uncertainty due to imprecision or vagueness. Its ability in representing vague data is considered as the major contribution of fuzzy set theory to science and technology. Multiple criteria decision making was introduced as a promising and important field of study in the early 1970'es. Since then the number of contributions to theories and models, which could be used as a basis for more systematic and rational decision making with multiple criteria, has continued to grow at a steady rate. Fuzzy optimization programming is a powerful technique to solve multi-objective decision making problems. An application of fuzzy optimization techniques to linear programming problems with multiple objectives has been presented by Bellman and Zadeh, and a few years later Zimmermann, (1978). Indeed introduction of fuzzy sets into the multi objective problems field cleared the way for a new attentions to deal with problems which had been inaccessible to and unsolvable with standard MCDM techniques. Several researchers (Buckley, 1985: Chiou, et al., 2005 state that fuzzy set theory has given a significant contribution by accepting uncertainty and inconsistent judgment as a nature of human decision making in the area of MCDM. Traditional AHP 1 is assumed that there is no interaction between any two criteria within the same hierarchy. However, a criterion is inevitably correlated to another one with the degrees in reality. In 1965, Zadeh introduced the concept of fuzzy measure and fuzzy integral, generalizing the usual definition of a measure by replacing the usual additive property with a weak requirement, i.e. the monotonic property with respect to set inclusion. In this section, we give a brief to some notions from the theory of fuzzy measure and MCDM. In this paper following to Gupta et al., (2000) applied Fuzzy Multi-Criteria Decision Model for planning of Crop pattern in Pishin river basin of Iran. It is clearly that there is no a single objective that satisfies all adversities, all interests, and all socioeconomic viewpoints. Hence, five objectives have been recognized to illustrate the potential methodology are: (i)benefit maximization, (ii)investment minimization, (iii)maximization of calories, (iv) labor employment and (v) maximize crop area. Therefore the considered objectives functions are: 1-Maximization of net benefit: considering the economic objective of net benefit maximization is commonly in the planning area problems and farmers often prefer cropping patterns which can provide more benefits. So mathematically it can formulate as:

2-Minimization of investment:
The objective like minimum investment is usually aspired to decision makers because it can plays significant role in agriculture of developing countries such as Iran; commonly farmers have financial problems and they prefer a cropping pattern which needs less investment so investment minimization can involved in the planning process. Hence: 3-Minimization of Water: Considering the government's policy of providing a water intensive cropping pattern to reduce water consumption in agriculture sector. Hence, it can be written as mathematically:

Model Constraints:
The model subjected to the seven constraints as follow: 1-Water requirement Considering the restriction of water requirement is commonly in the planning area problems and irrigation water demand of all the crops in any month is utmost equal to the total water available: Fuzzy programming is a powerful technique to solve multi-criteria decision making problems. The essentials of the approach are usually converting the multi-objective problem into a single objective problem. Generally for each objective function Z t (x) exist a determined efficient optimal solution x t so that: Also it can define Z t m as: Such that: Generalized fuzzy linear programming model The central idea behind fuzzy linear programming is that ill-defined problems are first formulated as fuzzy decision models. Crisp models can then be designed which are equivalent to the fuzzy models and could be solved by using existing standard algorithms. This approach is particularly suitable for decision problems which have the structure of linear programming. ( Gupta, et.al. 2000) Zimmermann (1978) introduced fuzzy programming approach to solve multi-objective linear programming problems and some researchers including Sakawa and Yano (1985), beside Leberling and Hannan (1981) have developed it to fuzzy multi-objective linear programming. In μ of this theory, the membership of the members of the set is being determined by function, which x is the representative of a known member and is a fuzzy function, that determines the membership degree of x in the relevant set and its quantity is between zero and one. Indeed the fuzzy objective function is characterized by its membership function, and membership function plays as substitute characterization of preference in determining the preferred outcome for each of the objectives. Membership function for the tth objective denoted by μZ(x) and should be have the following conditions:

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A point X is said to be an optimal solution to the FLPP if Z* for all x . The relationship between constraints and objective functions in a fuzzy environment is therefore fully symmetric, i.e. there is no longer a difference between the former and latter (Bellman and Zadeh, 1970). The fuzzy maximization problem can be defined as follows (Zimmermann, 1978;Leberling, 1981): Subject to ≤b Where at least one Xj≥0.
Consider a multiple objective optimization problem with k fuzzy goals f1 ,f2, …, fk represented by fuzzy sets i that all objective functions are characterized by corresponding membership functions. By generalizing the analogy from the single objective function, the resulting fuzzy decision is given as; In terms of corresponding membership values for the fuzzy goals that introduced Zadeh(1965), the resulting decision is; μ (x)= min (μZ1(x)… μZk(x)). Then all objectives should be satisfied simultaneously via its membership functions. Briefly for aggregate function can be defined as follow: μD(x) = μD ((μD Z1(x)… μD Zk(x)) and the general optimization problem will be changed to maximization of μD(x). An optimum solution X* is one at which the membership function of the resulting decision is maximum, that is, μ (X*) =max μ (X) Multi objective fuzzy linear programming model for crop area planning:

International Journal of Academic Research in Economics and Management Sciences
March 2014, Vol. 3, No. 2 ISSN: 2226-3624 In general, multi objective linear programming problem (MOLPP) refers to those FLP problems of systems in which multiple objectives to be controlled. For above FLPP, the multi objective fuzzy linear programming problem for crop area allocation can be formulated as follow: So this is exact to real-world, as marginal utilization of the decision maker decreases as the level of utilization (grade of membership) with respect to attainment of objective increases. Therefore, member function selection with hyperbolic nature is reasonable and chosen membership function for fuzzy goals of the decision maker presented as follow: Where , are value of Zt(x)* and a shape parameter, respectively, such that .
Z* t and Z tm are best and worst value of tth objective function, .
Generally fuzzy objectives of the decision maker together with using the hyperbolic membership function can be presented as follow: Max μ (x) = Max Subject to: (19) ≤b Where at least one Xj≥0 and . Leberling (1981) showed that and tan h(x) is a strictly monotone increasing function with respect to x, then the maximization of is equivalent to the maximization of xn+1. Hence, fuzzy vector valued multi-objective optimization problem can be transformed to the following crisp model:
The shape of the membership functions such as a linear, concave, or convex function, for various objectives and constraints, can affect the optimum solution significantly. Marginal utilization of the decision maker decreases as the level of utilization (grade of membership) with respect to attainment of objective increases. So, member function selection with hyperbolic nature seems correct. are said to be an optimal solution to the original problem if : So, the area allocation model with hyperbolic membership function can be written as follows: Max An+1

International Journal of Academic Research in Economics and Management Sciences
-Investment minimization: -Maximization of total area under irrigation: 3) Non negative constrains:

Result and discussion:
Agricultural sector pose many challenges that can be formulated as optimization problems such as crop selection and irrigation planning. Such decisions are made to achieve a certain objectives that typically include the maximization of net profit and/or the minimization of required investment. The problem is complicated by the existence of conflicted multi-objectives. Water management represents one of the most critical problems that face the national interests in the current and near future, especially in Iran. Given that agricultural irrigation water accounts for 80% consumption of the water resources, better agricultural systems management can play a critical role to solution of water crisis. Pishin reservoir is one of the major reservoirs in the Sarbaz river basin in west south of Pishin city and confluence place of Pishin and Sarbaz rivers with 175 million cubic meters.
Climate change scenarios of future temperature and rainfall levels under the socio-economic and ecological aspects have been produced for the Pishin river basin were selected from an ensemble of climate model (CGCM3T63) that simulates with respect to different trajectories of population growth, economic development and technological growth as A2, B1 and A1B emissions scenarios of the IPCC FAR (2007) that it will affect the level of future climate change and, simultaneously. Table (1). Simulations of changes in temperature and rainfall precipitation were introduced into a rainfall-runoff model to produce upstream flow projections. The combination of flow projections with different scenarios was used in a Fuzzy -linear programming model to produce water optimum allocation to competition sectors in the Pishin river basin. An economic model of agricultural water use is constructed using data available from crop cost and returns and land use observations for the area. The model aims are maximizing the profit and minimizing of investment and minimizing of water consumption. This model is used to explore the effect of temperature and rainfall variations on crop selection and cultivated area in study region. Furthermore, considering of climate changes effect on agricultural products yield is important. Any increasing temperatures or/and decrease in water availability lead to decreasing of potential yield for most crops probably. Although the actual impact of climate change on potential yields depends on the specific crop, ecological zone, and the farmer reaction. Changes in cropping patterns in terms of yield variations are also estimated within the model. It is also assumed that the region is a price-taker in agricultural markets; hence prices are assumed to be exogenous in the model.  As shown in Table (2), the various optimized cropping patterns compared versus the base year cropping pattern and exhibited under three climatic scenarios and different economic-environmental aspects. The allocated cropping area was different in the base year, the cropping pattern giving the priority to Rice, Clover, alfalfa, and Water Melon with a proximity allocated area equivalent to about 87.7% of the total cropping area whereas in FMCD model in A2, B1 and A1B climatic scenarios, optimized cropping patterns was given the priorities to Rice, Water melon, Bean and in B1 scenario Rice, bean, clover; A1B scenario Water melon, Rice, clover respectively. The greatest allocated area variations versus cultivated area in base period were about -50 percent in minimum consumption model under A1B climate change scenario and smallest variation quantity was about 0.36 % in A1B Scenario under investment minimization objective. Furthermore a considerable improvement was observed in cultivated area under A2 and B1 climate change scenarios in Fuzzy multi-Objective Decision (FMCD) about 38 and 18.5% whereas it extremely decreased in minimization of water consumption model under A2, B1 and A1B scenarios to 52, 48 and 50 % respectively. Table (2) So cropping pattern optimization of the considered crops in Pishin river basin of Iran in under the economical and environmental aspects and accordant to different objectives showed the great potential of Pishin River Basin to restructure its cropping pattern in accordance with its climate changes to generate a different net annual return in different climatic scenario.