Identifying Optimal Security Management Policy for Water–Energy–Food Nexus System under Stochastic and Fuzzy Conditions

: An interval-stochastic-fuzzy policy analysis model is proposed to generate optimal security management policy for a water–energy–food nexus system of the urban agglomeration under multiple uncertainties. A number of planning policies under interval-stochastic surface water and groundwater conditions are obtained. Ranking scores of all policies in descending order, policy with the highest score is the best choice. Results disclose that (a) interval-stochastic available water resources lead to changing system beneﬁts. (b) The shares of cropland area targets are 2.7% (Xiamen), 42.6% (Zhangzhou), and 54.7% (Quanzhou). (c) Di ﬀ erent available water scenarios result in varied irrigation patterns. (d) Surface water takes a high fraction of the total water supply (about [71.34, 73.68]%), diesel agricultural machinery service more than 60% of the total cropland. (e) Zhangzhou contributes about 50.01% of total TN and TP emissions, while Quanzhou contributes about 50.61% of total carbon emission. (f) Security level of policies would change with the varied σ and α values, due to the risk attitudes of policy makers. (h) Sweet potato and others are the crops with the highest safety performance; (i) Zhangzhou is the city with highest comprehensive safety performance.


Introduction
The water-energy-food nexus system represents a method to enhance the security and efficient management taking the inherent interactions into account [1]. Water is needed to make crops grow; electricity is required to collect, deliver, and treat water; energy (including electricity) is essential for harvesting and processing food; electricity generation needs water to cool machines; food waste can provide raw material for biomass energy [2][3][4]. Increasing resource interlinks due to growing scarcities, resources supply crises, and failures of sector-driven management strategies justified the need for the cross-sectoral integration of the resources [5]. Cities are sites of resources distribution, consumption, production, and recycling. A city often takes advantage of resources outside the city boundary, and then generates adverse environmental impacts inside other borders of cities. The idea behind the nexus is to look at the interdependent resource issues of water, energy, and food using an integrated framework in scientific analysis and policymaking. It is important to encompass the relationship between different resources in different cities, which formulate intricate water-energy-food nexus (WEF) systems. Global WEF securities (e.g., improved WEF policies lead to adaptive ecosystem and resource governance and management, in turn achieving sustainability outcomes) are facing unprecedented challenges from the fast speed of urbanization, increment of food demands, shortage of Water 2020, 12, 3268 4 of 23 Subject to: A ± X ± ≤ B ± (2) Q(X ± , ω ± ) = min q(Y ± , ω ± ) (3) T(ω ± )X ± + W(ω ± )Y ± ≤ H(ω ± ) (4) where X ± is first-stage decision variable (i.e., preset target); Y ± is second-stage decision variable (i.e., occurred event); ω ± is random variable defined in probability space (Ω ± , F ± , Pr); E is expectation values; C ± , A ± , and B ± are known coefficient matrices, T(ω ± ), W(ω ± ), and H(ω ± ) are functions of the random variable. The random variable can be discretized into a couple of certain interval values with associated probabilities to reflect the uncertainties [32]. The above ITSP can then be simplified as follows [33]: p h e ± j y ± jh (7) Subject to: x ± j ≥ 0 (10) y ± jh ≥ 0 (11) where ω ± h is random variables with discrete probability level p h ; h = 1, 2, . . . , H is the corresponding scenario. The ITSP model can be divided into two submodels as [34]: Upper-bound submodel: p h e − j y + jh (12) Subject to: 0 ≤ u j ≤ 1 (15) y + jh ≥ 0 (16) Water 2020, 12, 3268

Interval-Fuzzy Ordered Weighted Averaging Operator (IF-OWA)
For achieving more reasonable management policies, further analysis is needed from the perspective of multiple conflicting criteria (e.g., benefit, cost, pollutant, labor, and resource). IF-OWA is used for conducting policy analysis. IF-OWA can assess the system under a series of criteria, which is helpful for managers to select an optimal scheme based on their risk attitudes. There are two key factors in the assessing system: the criteria important degrees and corresponding quantified estimated objectives [35]. The first factor is often expressed as linguistic variables based on experts' subjective consciousness. The second factor is generally known to fall within a certain interval [36]. The method adopts fuzzy logic approach to handle the linguistic information and takes interval theory to dispose the estimated objectives. The solution process includes reordering the inputs in descending order, determining the weighting vector, and aggregative procedure.
The first step is to handle all criteria to formulate new inputs. This step needs to be conducted after obtaining detailed data of all criteria (i.e., results of the ITSP model). The estimated criteria are presented as interval numbers [37]: where x + and x − represent the optimistic and pessimistic data for the positive criterion, and vice versa. α ∈ [0, 1] represents the optimism degree of the decision maker, a higher α corresponds to a more optimistic attitude of the decision maker. Since all criteria have different units, they are necessary to be normalized as follows: where x max i and x min i are the maximum and the minimum values in criterion i, respectively. The new inputs can be obtained through multiplying x * ij by normalized crisp data of important degree. Five important degrees (d) are selected as unimportant, marginal important, moderate important, quite important, and extremely important. They are expressed as triangular fuzzy members, and transformed as normalized triangular fuzzy members [38]. For example, for moderate important degree, the normalized triangular fuzzy number is Z (0.50, 0.25, 0.25), the membership degree is f z (0.50) = 1, and the left-and right-benchmarks of 0.50 are 0.25 and 0.25. Center of gravity method is then adopted to convert the normalized triangular fuzzy number into crisp data (i.e., (0.25 + 0.50 + 0.75) / 3 = 0.50). Exact values of important degrees are obtained. The normalized fuzzy members of five important degrees are 0.13, 0.25, 0.50, 0.75, and 0.87. The next step is to identify weighting vectors of all criteria. Different σ (σ ∈ [0, 1]) values denote deferent satisfactions to criteria considered in the decision-making system. σ = 0 means that only the minimal element in the inputs can be satisfied, and σ = 1 denotes that only the maximal element in the inputs can be satisfied. The weighting vector can be calculated as follows [39]: The integrated score of an alternative policy can be calculated based on Equation (27). Ranking scores of all policies in descending order, the policy with the highest F j is the best choice:

Study Area Description
The Xiamen-Zhangzhou-Quanzhou urban agglomeration (24 • Figure 1). It is one of the most important urban agglomerations in China, as well as the largest Metropolitan Area in Fujian Province in terms of both surface area and population (supported 51.4% of the provincial population and contributed 51.1% provincial population gross domestic products) [40][41][42][43][44]. The agglomeration is subjected to a typical subtropical ocean monsoon climate; the average annual rainfall is 1200-1800 mm, total annual solar radiation is 120-140 kcal/cm 2 , and average temperature is about 19.5-21.0 • C. It contributes 18.46% of the total grain production with 33.64% of land area, 45.62% of cultivated land, 40.01% of water resources, and 37.81% of energy resources in the province [43].
Water 2020, 12, x FOR PEER REVIEW 6 of 25 minimal element in the inputs can be satisfied, and σ = 1 denotes that only the maximal element in the inputs can be satisfied. The weighting vector can be calculated as follows [39]: The integrated score of an alternative policy can be calculated based on Equation (27). Ranking scores of all policies in descending order, the policy with the highest j F is the best choice:

Study Area Description
The Xiamen-Zhangzhou-Quanzhou urban agglomeration (24°28′55.77″ N-24°52′36.45″ N and 117°38′32.84″ E-118°40′16.72″ E) is located at southeast of Fujian Province in south China, with an area of approximately 25,314.17 km 2 (in Figure 1). It is one of the most important urban agglomerations in China, as well as the largest Metropolitan Area in Fujian Province in terms of both surface area and population (supported 51.4% of the provincial population and contributed 51.1% provincial population gross domestic products) [40][41][42][43][44]. The agglomeration is subjected to a typical subtropical ocean monsoon climate; the average annual rainfall is 1200-1800 mm, total annual solar radiation is 120-140 kcal/cm 2 , and average temperature is about 19.5-21.0 °C . It contributes 18.46% of the total grain production with 33.64% of land area, 45.62% of cultivated land, 40.01% of water resources, and 37.81% of energy resources in the province [43]. Currently, expansion in urban capacity, variation in natural conditions, adjustment in land use, and fluctuation in resources demand lead to changing water-energy-food nexus structure of the agglomeration. For example, irrigation water keeps decreasing with a declined rate of 4.11%; cropland area keeps decreasing with a declined rate of 4.22%; fossil energy consumption keeps decreasing with a declined rate of 1.31%; electric energy keeps increasing with a growth rate of 3.72%; population keeps increasing with a growth rate of 7.33%; value-added rate of agriculture keeps decreasing with a declined rate of 1.81% [43]. Apparently, population growth leads to increasing food Currently, expansion in urban capacity, variation in natural conditions, adjustment in land use, and fluctuation in resources demand lead to changing water-energy-food nexus structure of the agglomeration. For example, irrigation water keeps decreasing with a declined rate of 4.11%; cropland area keeps decreasing with a declined rate of 4.22%; fossil energy consumption keeps decreasing with a declined rate of 1.31%; electric energy keeps increasing with a growth rate of 3.72%; population keeps increasing with a growth rate of 7.33%; value-added rate of agriculture keeps decreasing with a declined rate of 1.81% [43]. Apparently, population growth leads to increasing food demand and electric energy (for daily life), low water resources first satisfy electricity generation and limited irrigation water supply; food should be imported from other regions, thus reduce the economic output. Decision makers pay much attention to the issues of making a reasonable cropland, water, and energy planning policy to satisfy water-energy-food nexus security, economic development, and environment requirement.

System Boundary and Components
Urban agglomeration is a complex system consisting of social, economic, environmental, and resource factors. An interval-stochastic-fuzzy policy analysis (ISF-PA) model which couples ITSP and IF-OWA models is formulated to support WEF security under multiple uncertainties. The framework of the ISF-PA model is presented in Figure 2.
Water 2020, 12, x FOR PEER REVIEW 7 of 25 economic output. Decision makers pay much attention to the issues of making a reasonable cropland, water, and energy planning policy to satisfy water-energy-food nexus security, economic development, and environment requirement.

System Boundary and Components
Urban agglomeration is a complex system consisting of social, economic, environmental, and resource factors. An interval-stochastic-fuzzy policy analysis (ISF-PA) model which couples ITSP and IF-OWA models is formulated to support WEF security under multiple uncertainties. The framework of the ISF-PA model is presented in Figure 2. The study system is composed of (i) seven crops including early rice, middle rice, late rice, sweet potato, potato, soybean, and others; (ii) two water sources including surface water and groundwater; (iii) three energy sources including gasoline, diesel, and electricity; (iv) three emissions including carbon dioxide (CO2), total phosphorus (TP), and total nitrogen (TN); (v) two chemicals: pesticide and fertilizer; (vi) three cities: Xiamen, Zhangzhou, Quanzhou. Decision making processes should  The study system is composed of (i) seven crops including early rice, middle rice, late rice, sweet potato, potato, soybean, and others; (ii) two water sources including surface water and groundwater; (iii) three energy sources including gasoline, diesel, and electricity; (iv) three emissions including carbon dioxide (CO 2 ), total phosphorus (TP), and total nitrogen (TN); (v) two chemicals: pesticide and fertilizer; (vi) three cities: Xiamen, Zhangzhou, Quanzhou. Decision making processes should fully consider market situation, water requirement and availability for irrigation, electricity demand for water collection and delivery, energy demand for machinery operation, energy availability, land use policy, effluent and carbon emission, labor employment, and food guarantee, as well as represent the complexities and interactions among them. Meanwhile, economic and technological parameters vary with market fluctuations, subjective judgments of experts affect data acquisition and system reliability, spatiotemporal variability of runoff leads to changed available water resources, food demand increases with population growth, arable land area and food types affect energy consumption. The uncertainties are quantified as interval, stochastic, and fuzzy variables.

Modelling Formulation
In the first stage, decision makers set initial targets of all crops in each city without catching available water resources conditions. In the second stage, random available water resources conditions are recognized. If targets are too high, local resources may not be sufficient to satisfy demand. Decision makers need to extract groundwater more deeply (which is harmful for aquifers). If targets are too low, local citizens may withstand economic losses. Infeasibilities in the second stage are allowed at a certain penalty (i.e., the second-stage decision is used to minimize penalty that may appear due to any infeasibility). A number of management policies related to cropland area, water allocation, and energy consumption can be obtained based on the ITSP model as follows: Objective function: where c is index of crop; s is index of city; h 1 is available surface water level (h 1 = 1 for low, h 1 = 2 for medium, h 1 = 3 for high); h 2 is available groundwater level (h 2 = 1 for low, h 2 = 2 for medium, h 2 = 3 for high); MP ± c,s is market price (Yuan/kg); CA − c,s is lower bound of cropland area target that should be irrigated by water and cultivated by energy agricultural machine (ha); ∆CA ± c,s is the difference between upper and lower bounds (ha); x ± c,s is decision variables for destemming cropland area target in first-stage; CY ± c,s is unit crop yield (kg/ha); p h is probability of available water occurrence under level h; CSW ± s is unit cost of surface water (Yuan/m 3 ); CAS ± c,s,h 1 is cropland area irrigated by surface water (ha); IQR ± c is irrigation quota (m 3 /ha); CGW ± s is unit cost of groundwater (Yuan/m 3 ); CGS ± c,s,h 2 is cropland area irrigated by groundwater (ha); CF ± s is unit cost of fertilizer (kg/ha); CP ± s is unit cost of pesticide (Yuan/kg); CAF ± s is unit cost of agricultural film (kg/ha); CD ± s is unit cost of diesel (Yuan/liter); AD ± c,s is unit diesel consumption of cropland (liter/ha); CDA ± c,s is cropland area cultivated by diesel agricultural machinery (ha); CGA ± c,s is cropland area cultivated by gasoline agricultural machinery (ha); CEA ± c,s is cropland area cultivated by electric agricultural machinery (ha); CG ± s is unit cost of gasoline (Yuan/liter); AG ± c,s is unit gasoline consumption of cropland (liter/ha); CE ± s is unit cost of electricity (Yuan/kWh); AE ± s is unit electricity consumption for cropland (kWh/ha); UED ± is unit electricity consumption for surface water (kWh/m 3 ); UEG ± is unit electricity consumption for groundwater (kWh/m 3 ); Water 2020, 12, 3268 9 of 23 Constraints: (1) Surface water availability: Surface water delivered to all the crops in each city should not be higher than available surface water supply.
(2) Groundwater availability: Groundwater allocated to all the crops in each city should not be higher than allowable groundwater pumping.
(3) Energy availability: The energy consumption for crop cultivation should not be higher than the available energy for agriculture in each subarea.
(4) Food security: The yield of food grain for each subarea should satisfy the food grain requirement that is associated with population in order to guarantee food security.
(5) Cropland area: Cropland area should not be higher than the maximum value and lower than minimum value. All cropland should be irrigated by water and cultivated by energy agricultural machine.
(6) Total nitrogen emission: Nitrogen emission by fertilizer application should not be higher than the allowable amount.
(7) Total phosphorus emission: Phosphorus emission by fertilizer application should not be higher than the allowable amount.
Water 2020, 12, 3268 10 of 23 (8) Agricultural film utilization: Agricultural film utilization often causes plastic environmental pollution, which needs to be controlled.
(9) Pesticide utilization: The spraying of pesticides often brings about COD and eutrophication environmental pollution, which must not exceed the allowable value.
(10) Carbon emission: Excessive CO 2 emission can lead to greenhouse effect. It is important to control CO 2 emission.
(11) Labor employment: The amount of labor is limited due to the budget.
(12) Non-negative variable: Since this is a real-world case study, all variables should be non-negative. Through running the proposed model, solutions of all decision variables can be obtained. System benefit can then be determined.
is available groundwater (m 3 ); ADM ± s is available diesel supply (liter); AGM ± s is available gasoline supply (liter); AEM ± s is available electricity supply (kWh); PP ± s is number of population (person); FD ± is per food demand (kg/person); CA ± c,s(min) is minimum cropland area (ha); CA ± c,s(max) is maximum cropland area (ha); FA ± c,s is unit fertilizer application (kg/ha); NC ± is total nitrogen content of fertilizer (kg N/kg); η ± s is loss rate of total nitrogen (%); TNE ± s is allowable total nitrogen loss (kg N); PC ± is total phosphorus content of fertilizer (kg P/kg); λ ± s is loss rate of total phosphorus (%); TPE ± s is allowable total phosphorus loss (kg N); FU ± s is unit agricultural film application (kg/ha); TFU ± s is total allowable agricultural film application (t); PU ± c,s is unit pesticide application (kg/ha); TPA ± s is total allowable pesticide application (t); α ± 1 is carbon emission of diesel (kgCO 2 / liter); α ± 2 is carbon emission of gasoline (kgCO 2 / liter); α ± 3 is carbon emission of electricity (kgCO 2 /kg); α ± 4 is carbon emission of fertilizer (kgCO 2 /kg); α ± 5 is carbon emission of film (kgCO 2 /kg); α ± 6 is carbon emission of pesticide (kgCO 2 /kg); TCE ± s is total allowable carbon emission (kg); LAM ± s is number of labor (person/ha); WG ± is unit remuneration (Yuan/person); TWG ± s is total remuneration (Yuan). Table 1 shows the interval values of different cities and crops. Market prices were obtained from the "Agricultural Product Price Information Network of Fujian Province"; Crop yields were gained from "Statistical Yearbook" of each city; irrigation quotas were obtained from "Standard Local Water Quota of Fujian Province"; unit diesel, fertilizer, and pesticide application were extracted from "Agricultural Information Network" of the cities. Other parameters were obtained from field research and published references [33,45,46]. Tables 2 and 3 present the values of stochastic surface water and groundwater (e.g., population growth and the expansion of urban areas impacted the groundwater level and its salinity, leading to changed groundwater availability) in the cities, which were collected from the "Water Resources Bulletin" of the cities [47,48]. Combinations of different available surface water and groundwater levels lead to six scenarios. For instance, for scenario 1 (i.e., S1), low (p h 1 = 0.23), medium (p h 1 = 0.56), and high (p h 1 = 0.21) levels of surface water correspond to low (p h 2 = 0.28), high (p h 2 = 0.57), medium (p h 2 = 0.25) levels of groundwater.       The IF-OWA method was then employed to assess the system security according to decision makers' optimism degrees. Ten criteria including CY, CA, MP, IQR, CAS, CGS, AD, AG, FA, and PU were selected, which were determined after running the ITSP model. Table 4 presents the weighting vectors (w i ) of the 10 criteria under each σ value. Important degrees of criteria are represented as linguistic quantifiers (L for "low", LM for "low-medium", M for "medium", MH for "medium-high", and H for "High"). The linguistic important degrees of the criteria were converted into their equivalent triangular fuzzy numbers and transferred into crisp normalized values. Table 5 presents defuzzied linguistic quantifiers (d i ), in which the normalized values of five important degrees are 0.1333, 0.2500, 0.5000, 0.7500, and 0.8667. Ten criteria can be handled based on Equation (23) to formulate new inputs. Lower bounds represent optimistic data for positive criteria, while lower bounds represent pessimistic data for negative criteria. For instance, market price of early rice is [2.28, 3.12] Yuan/kg in Xiamen, which means that high market price can lead to high benefit (i.e., optimistic condition). Cost of surface water is [2.32, 1.82] Yuan/m 3 in Xiamen, which denotes that high cost of surface water can result in low benefit (i.e., pessimistic condition). All criteria should be normalized (x * ij ) using Equation (6) Figure 3 shows revenues and costs of each city as well as system benefit (i.e., f = total revenue minus total cost) under each scenario. Results show that the lowest f would be [8.9,  A cropland area target is pre-regulated for each crop in each city before the amounts of random available water resources are known. Figure 4 displays the optimal cropland area target. Total cropland area of the cities would be 2605.42 × 10 3 ha (with Xiamen 2.7%, Zhangzhou 42.6%, and Quanzhou 54.7%). This may be attributed to the rapid urban construction of Xiamen, leading to the shrinking of cropland area. The development of Zhangzhou and Quanzhou still heavily rely on crop cultivation. The proportions of early rice and late rice would be 29.7% and 27.6%, respectively. This may be associated with climatic conditions, soil properties, market prices, and crop yields. Cropland area in sweet potato, soybean, and others in Quanzhou would be set as their upper bounds (i.e., x = 1), indicating decision makers take optimistic attitudes (due to high crop yields and market prices).    A cropland area target is pre-regulated for each crop in each city before the amounts of random available water resources are known. Figure 4 displays the optimal cropland area target. Total cropland area of the cities would be 2605.42 × 10 3 ha (with Xiamen 2.7%, Zhangzhou 42.6%, and Quanzhou 54.7%). This may be attributed to the rapid urban construction of Xiamen, leading to the shrinking of cropland area. The development of Zhangzhou and Quanzhou still heavily rely on crop cultivation. The proportions of early rice and late rice would be 29.7% and 27.6%, respectively. This may be associated with climatic conditions, soil properties, market prices, and crop yields. Cropland area in sweet potato, soybean, and others in Quanzhou would be set as their upper bounds (i.e., x = 1), indicating decision makers take optimistic attitudes (due to high crop yields and market prices).   The targeted croplands are irrigated by surface water and groundwater. Figures 5 and 6 summarize the optimal irrigation patterns of different crops under various available water scenarios. The proportion of cropland irrigated by surface water would be about [71.3, 73.8]%. This is mainly because of the high available surface water. Different scenarios would result in varied irrigation patterns. For instance, under S1, the area irrigated by surface water and groundwater would be [1877. 8,1967.2] × 10 3 ha (low level) and [638.2, 727.6] × 10 3 ha (low level); under S4, the area irrigated by surface water and groundwater would be [1852. 6,1926.6] × 10 3 ha (low level) and [669.5, 762.1] × 10 3 ha (medium level). It is found that Zhangzhou would be the most sensitive city to the changed available water resources (other cropland irrigation patterns would not change), due to relatively high cropland, limited water resources, and high demand of electricity for surface water. Under a certain scenario, irrigation patterns would also change with the varied available water level. For instance, under S6, the area irrigated by surface water would be [1831.0, 1885.6] × 10 3 ha, [1843. 3,1935.9] × 10 3 ha, and [1871.9, 1988.9] × 10 3 ha under low, medium, and high levels, respectively. It is disclosed that surface water is more competitive than groundwater. This is associated with water price, irrigation quota, and available water.

Management Policy
available water resources (other cropland irrigation patterns would not change), due to relatively high cropland, limited water resources, and high demand of electricity for surface water. Under a certain scenario, irrigation patterns would also change with the varied available water level. For instance, under S6, the area irrigated by surface water would be [1831.0, 1885.6] × 10 3 ha, [1843. 3,1935.9] × 10 3 ha, and [1871.9, 1988.9] × 10 3 ha under low, medium, and high levels, respectively. It is disclosed that surface water is more competitive than groundwater. This is associated with water price, irrigation quota, and available water.   Figure 7 shows the optimal water allocation policy. It is found that surface water would take a high fraction of the total water supply (approximately [71. 34,73.68]%). Groundwater with higher water price and lower availability would be considered as a flexible supplementary resource to guarantee water safety for crop production under random available levels. Water allocated to early rice and late rice would, respectively, be [31.17, 31.53]% and [35.46, 36.12]% of the total water supply, due to their high cropland area targets and irrigation quota. Figure 8 lists the optimal energy consumption policy. Diesel agricultural machinery would share a large proportion of tillage, irrigation, drainage, and harvesting (serving for more than 60% of the total cropland area). The optimal energy consumption amount would be   consumption policy. Diesel agricultural machinery would share a large proportion of tillage, irrigation, drainage, and harvesting (serving for more than 60% of the total cropland area). The optimal energy consumption amount would be [97.4, 100.3] × 10 3 L of diesel (liter), [38.9, 40.1] × 10 3 L of gasoline, and [19.4, 20.9] × 10 3 kWh of electricity (a proportion of [4.23, 5.01]% would contribute to water allocation). Zhangzhou would be the main energy consumer, which would consume [51.23, 52.12]% of the total energy.      Zhangzhou would contribute the highest emissions of TN and TP (occupying about 50.01% of the total emission), due to relatively high loss rate and unit fertilizer/pesticide application. The sources of carbon emission include diesel, gasoline, electricity, fertilizer, agricultural film, and pesticide. Quanzhou would contribute the highest emissions of CO 2 (occupying about 50.61% of the total emission), due to relatively high cropland area. In addition, decision makers should focus on early rice, late rice, and sweet potato. The emissions would account for more than 77.21% (TN), 77.45% (TP), 77.68% (CO 2 ) of the total emissions. This revealed a tradeoff between economic development and environmental protection.
In addition, under σ = 0.33, sweet potato, others, potato, and soybean of Xiamen are in the top four ranks; under σ = 0.43, sweet potato of Xiamen, sweet potato of Quanzhou, others of Xiamen,

Policy Security Assessment
All new inputs of the IF-OWA method can then be calculated. As an example, Table 6 displays new inputs under α = 0.5. Figure 10 9,19,20,1,4,8,3,13,21,18,17,16,15,6,10,17,11,2,14,12 9, 20, 19, 14, 8, 3, 14, 21, 18, 17, 16, 15, 6, 10, 17, 12, 2, 13, 11, and 7) under α = 0.9. Higher α values represent more progressive attitudes of decision makers (while higher risk levels of suffering system infeasibility), and thus more croplands, less investments, and less resources would be put to use in order to meet local demand. In addition, under σ = 0.33, sweet potato, others, potato, and soybean of Xiamen are in the top four ranks; under σ = 0.43, sweet potato of Xiamen, sweet potato of Quanzhou, others of Xiamen, potato of Xiamen are in the top four ranks; under σ = 0.53, sweet potato of Quanzhou, sweet potato of Xiamen, sweet potato of Zhangzhou, others of Zhangzhou are in the top four ranks; under σ = 0.63, sweet potato of Quanzhou, sweet potato of Zhangzhou, others of Zhangzhou, early rice of Zhangzhou are in the top four ranks. Sweet potato and others would be the crops with the highest safety performance (especially sweet potato). This may be derived from their high market price, high crop yield, and low irrigation quota. Zhangzhou would be the city with highest comprehensive safety performance, due to the high revenue. The decision maker can select the final optimal alternative according to his/her risk tolerance.

Discussion
Th main findings can be summarized as follows: (a) the interactions between available surface water and groundwater can change the irrigation patterns and thus affect the system benefit. System benefit would increase by [2.34, 165.16]% from the lowest value to the highest value. (b) The shares of cropland area targets are 2.7% (Xiamen), 42.6% (Zhangzhou), and 54.7% (Quanzhou). (c) Early rice and late rice are main water consumers (occupying [31.17, 31.53]% and [35.46, 36.12]% of the total water supply). (d) More than 60% of the total cropland area were served by diesel agricultural machinery. (e) Zhangzhou is the most sensitive city to the changed available water resources. (f) Zhangzhou contributes 50.01% of the total TN and TP emissions, while Quanzhou contributes 50.61% of the total CO 2 emission. (g) Security level of cities and crops change with the varied σ and α values. Decision makers may need to (i) prepare emergency plans in case of low available water resources. (ii) Ensure sufficient water supply to early rice and late rice. (iii) Enhancement policies such as changing topographic slope, improving soil quality, promoting cropland drainage, and using energy-mix machine should be conducted. (iv) Pay attention to the development in the Zhangzhou city. (v) Conduct security assessment before making decisions.
The developed ISF-PA model can be applied to coordinate food production, water resource allocation, and energy consumption in a sustainable manner. A shortcoming of the model is that it can only account for the expected second-stage cost without any consideration on the variability of the cost under a certain available water level, such that Quanzhou suffers economic deficits. This may be unacceptable for local policy makers. Financial risk management methods are attractive techniques that could help tackle the above shortcoming, which is launched to control the variability of the recourse cost, as well as to capture the notion of risk. The impacts of other environmental policies such as carbon mitigation, air pollution control, water pollutant should also gain more concern. This is the first attempt to apply the developed model in the study area. It was difficult to compare current results with the other authors. In future works, comparison is needed since it can highlight the innovations of the current research.

Conclusions
In this study, an interval-stochastic-fuzzy policy analysis (ISF-PA) model was proposed to generate optimal security management policy for a water-energy-food nexus system. The model was applied to a practical study of a comprehensive issue in the Xiamen-Zhangzhou-Quanzhou urban agglomeration, Fujian province, China. In the application, surface water and groundwater availability were expressed as probability distributions; linguistic quantifiers were presented as triangular fuzzy membership functions; others were shown as interval values. The developed model provides the optimal policies of cropland planning, water allocation, energy consumption, as well as carbon and effluent emissions; meanwhile, the system security of different crops in different cities were evaluated.