An Interval Fuzzy, Double-Sided, Chance-Constrained Stochastic Programming Model for Planning the Ecological Service Value of Interconnected River Systems

: The western region of Jilin Province is an ecologically fragile area with scarce water resources. The e ﬀ ective allocation of the limited water resources in order to obtain a higher ecological service value is an urgent requirement. In this paper, an interval fuzzy, double-sided chance-constrained, stochastic programming (IFDCP) model was used based on the interconnected river system network project in the western Jilin Province. With the objective of maximizing the value of regional ecological services, the water diversion and supplement schemes were optimized and adjusted. The model results showed that the restored water surface area of all lakes and ponds in the western region of Jilin Province was higher than the initially planned scheme in the high ﬂow year. The water surface area fulﬁlled the minimum constraints, but did not fulﬁll the initial scheme in the normal ﬂow year. In the low ﬂow year, the lower limit of some of the regions had to be decreased in order to meet the allocation of the limited water resources. The proportion of ﬂoodwater resource utilization gradually increased with an increase in the ﬂood amount. The ecological service value produced in the normal and high ﬂow years was found to be higher than the initial scheme. The marsh wetland can produce higher ecological service value. Therefore, the core of the model optimization was introducing more water to the marsh wetland after fulﬁlling the basic consumption of ponds and the reed wetland. In addition, the IFDCP model was more ﬂexible in water diversion and supplement as compared to other models that had been developed previously.


Introduction
The western Jilin Province is located in the Songnen Plain, and it is an ecologically fragile area with little rainfall, serious soil salinization, and a sensitive ecological environment [1]. The interconnected river system network project can improve the self-healing ability of the water body by enhancing fluidity and continuity, and can realize the long-term health and stability of the water body [2]. Water ecological services are primarily the ecological value and the economic value of water resources [3], which are the benefits that organisms directly or indirectly obtain from ecosystems [4]. The wetland ecosystem is one of the most significant ecosystems on Earth [5]. Only covering 6% of the total terrestrial ecosystem area, wetlands can produce about 45% of the ecological service value of the total terrestrial ecosystem

Case Study
The study area includes the western Jilin Province, including Songhua River, Nenjiang River, Taoer River, and Huolin River, as well as 15 counties and districts. The total area is 4.46 × 10 4 km 2 . There are four national nature reserves: Xianghai, Momoge, Chagan Lake, and Boluo Lake. The Xianghai Nature Reserve primarily aims at protecting rare waterfowl, such as the red-crowned crane, and rare plant communities, such as the Mongolian yellow elm. The Momoge Nature Reserve is the largest wetland reserve in Jilin Province, known as the kidney of the western Jilin Province. The Chagan Lake is the largest natural lake in Jilin Province. The sketch map of western Jilin Province is shown in Figure 1.
Chagan Lake is the largest natural lake in Jilin Province. The sketch map of western Jilin Province is shown in Figure 1.

Ecological Service Value Optimization Model, Based on the Interval, Double-Sided, Chance-Constrained Stochastic Programming Model
This paper aims to maximize the ecological service value by optimizing the utilization and distribution of water resources of the interconnected river system network project in the western Jilin Province. The amount of flood resources and the ecological water demand are random, with the influence of rainfall, climate, etc. The chance-constrained stochastic programming method was adopted, and the randomness of flood resources was completely followed. Besides, all parameters were considered uncertain, with the characteristics of up-and-down fluctuations in the process of contributing to the ecological service value. The parameter values were set within a reasonable interval after comprehensively considering the uncertainty of all parameters. Then, the interval linear programming method was introduced. The diversion and supplement plan of water resources was obtained by using interval, double-sided, chance-constrained stochastic programming (IDCP), and the objective function is determined as follows: where f ± represents the interval value of ecological service value of the region of the interconnected river system network project, i represents the 198 lakes and ponds of the western Jilin Province, j represents different types of functions of the lakes and ponds ( j = 1, 2, 3, and 4 represents the fish pond, crab pond, reed wetland, and marsh wetland, respectively), k represents different types of ecological services, ijk EBW ± represents the interval value of the ecological service value of the ecological service k of the function j in the lake and pond i (10 6 CNY/10 4 ha), and

Ecological Service Value Optimization Model, Based on the Interval, Double-Sided, Chance-Constrained Stochastic Programming Model
This paper aims to maximize the ecological service value by optimizing the utilization and distribution of water resources of the interconnected river system network project in the western Jilin Province. The amount of flood resources and the ecological water demand are random, with the influence of rainfall, climate, etc. The chance-constrained stochastic programming method was adopted, and the randomness of flood resources was completely followed. Besides, all parameters were considered uncertain, with the characteristics of up-and-down fluctuations in the process of contributing to the ecological service value. The parameter values were set within a reasonable interval after comprehensively considering the uncertainty of all parameters. Then, the interval linear programming method was introduced. The diversion and supplement plan of water resources was obtained by using interval, double-sided, chance-constrained stochastic programming (IDCP), and the objective function is determined as follows: where f ± represents the interval value of ecological service value of the region of the interconnected river system network project, i represents the 198 lakes and ponds of the western Jilin Province, j represents different types of functions of the lakes and ponds ( j = 1, 2, 3, and 4 represents the fish pond, crab pond, reed wetland, and marsh wetland, respectively), k represents different types of ecological services, EBW ± ijk represents the interval value of the ecological service value of the ecological service k of the function j in the lake and pond i (10 6 CNY/10 4 ha), and FA ± ij represents the interval value of the supplement area of the function j in the lake and pond i (10 4 ha). The implementation of the IFDCP model needs to be limited by area, water amount, and so on, so constraints need to be set to ensure the rationality of the optimization results. This paper is based on existing studies, and retained the previous constraints for further comparison and analysis. The constraints include the total water amount, the water amount of lake and pond, and the area of lake and pond. Besides, the water diversion and supplement have priority; for example, the water requirements for fish and crab ponds and reed wetland should be met first. The constraints are as follows: (1) Constraints for water diversion and supplementation order: where m represents the source of the diversion and supplement of water (m = 1, 2, and 3 represents the local water resources, normal supplement, and flood resources, respectively), Q ± im is the interval value of the incoming water amount of water source m (10 4 m 3 ), QL ± im is the interval value of the water loss of the water source m of the lake and pond i (10 4 m 3 ), QW ± i is the interval value of the wetland water consumption of the lake and pond i (10 4 m 3 ), AP ± i is the interval value of the water surface area of the lake and pond i (10 4 ha), QWR ± i is the interval value of the unit water demand quota of the lake and pond i (10 4 m 3 /10 4 ha), AP ± mini is the interval value of the minimum water surface area of the lake and pond i (10 4 ha), QP ± ij is the interval value of the unit water demand quota of the function j of the lake and pond i (10 4 m 3 /10 4 ha), and FA ± mini3 is the interval value of the minimum supplement area of the reed wetland in the lake and pond i (10 4 ha); (2) Constraints for functional area: where FA ± maxij is the interval value of the maximum supplement area of the reed wetland in the lake and pond (10 4 ha); (3) Constraints for the diversion and supplement of water amount: (4) Constraints for the total water amount: where r represents 15 administrative regions for project water diversion and supplement, QT r ± is the interval value of the effective flood resources in the area r (10 4 m 3 ), RF r ± is the interval value of precipitation in the area r (10 4 m 3 ), θ ± r is the interval value of the probability of violating the constraint, and ω represents the randomness of relevant parameters.

Ecological Service Value Optimization Model Based on the Interval Fuzzy, Double-Sided, Chance-Constrained Stochastic Programming
The area of water surface and wetland has fuzzy uncertainty, and the fuzzy method was introduced to optimize the programming, in order to achieve the maximum value of the ecological service value.
The minimum values of the water surface area, functional area, and total area were set as fuzzy variables. The diversion and supplement plan of water resources was obtained by using the IFDCP, and the objective function is calculated as follows: where λ ± is the interval value of the fuzzy membership. The constraints are where f + and f − are the upper and lower bounds obtained from the IDCP. The IFDCP model also include the following: (1) Constraints for water diversion and supplementation order: (2) Constraints for the functional area: (3) Constraints for the diversion and supplement of water amount: (4) Constraints for the total water amount: Water 2020, 12, 2649

Model Parameters
The parameters for establishing the IFDCP model were adopted from previous studies [2,15], and the original parameters were reasonably adjusted to be interval parameters within a certain range. The Lingo software was used to solve the model. First, the IDCP model was solved, and the optimization scheme for the water diversion and supplement of the low flow year, normal flow year, and high flow year was obtained. Then, the fuzzy programming was applied to further optimize the interval results. Finally, the optimization scheme of the IFDCP was obtained. The flow chart of IFDCP model is shown in Figure 2.

Model Parameters
The parameters for establishing the IFDCP model were adopted from previous studies [2,15], and the original parameters were reasonably adjusted to be interval parameters within a certain range. The Lingo software was used to solve the model. First, the IDCP model was solved, and the optimization scheme for the water diversion and supplement of the low flow year, normal flow year, and high flow year was obtained. Then, the fuzzy programming was applied to further optimize the interval results. Finally, the optimization scheme of the IFDCP was obtained. The flow chart of IFDCP model is shown in Figure 2.

Results of the Restored Area of Wetlands, Lakes, and Ponds Based on the IFDCP
The system was divided into three scenarios (low flow year, normal flow year, and high flow year) according to the differences in the flood water amount at different times of the western Jilin. The three scenarios were optimized for the ecological services based on the IFDCP. In the three scenarios, the interval fuzzy memberships were 0.007-1.000, 0.030-0.960, and 0.090-0.870, respectively. The restored water surface area (fishpond area and crab pond area) and wetland area (reed wetland and marsh wetland) in the three scenarios are shown in Tables 1 and 2 and Figure 3.  0.14 0-0.14 0.14-0.14 0.14-0.14 0.36 0.

Results of the Optimization of Water Diversion and Supplement Based on the IFDCP
The change in the trend of the water diversion and supplement of ponds and wetlands was found to be consistent with the restored area. The supplement amount of water in the three water scenarios of the ponds was 60,670. The diversion and supplement of water were divided into local water resources, normal supplement, and flood resources. The water supplement amount in each scenario is shown in Figure  4. The change rates of the supplement amount of the total local water resources, as compared to the initially planned scheme in the three scenarios, were −8.68% to 1.08%, −3.35% to 1.98%, and −3.39% to 1.92%, respectively. The change rates of the normal supplement amount, as compared with the initially planned scheme in the three scenarios, were −0.77% to 4.96%, −0.15% to 5.02%, and −0.16% to 3.12%, respectively. The change rates of the supplement amount of flood resources, as compared with the initially planned scheme in the three scenarios, were −51.79% to −40.53%, 1.02% to 3.68%, and 17.57% to 21.36%, respectively. The total restored water surface areas of the lakes and ponds in the three scenarios were (10.73-11.71) × 10 4 , (12.44-12.65) × 10 4 , and (13.16-13.95) × 10 4 ha, respectively, which were changed from the initially planned schemes of −17.69% to −10.18%, −4.6% to −2.97%, and 0.92% to 7.01%, respectively. The total restored water surface area of the normal flow year and the high flow year increased by 8.03-15.9% and 19.14-22.61%, respectively, compared with the low flow year. The proportions of the restored fishpond area in the three scenarios, which were changed from the initially planned scheme, were −34.93% to −7.58%, 0.43% to 1.37%, and 6.84% to 15.24%, respectively. The proportions of the restored crab pond area in the three scenarios, which were changed from the initially planned scheme, were −7.76% to 1.31%, 2.51% to 7.46%, and 10.86% to 14.83%, respectively.

Results of the Optimization of Water Diversion and Supplement Based on the IFDCP
The change in the trend of the water diversion and supplement of ponds and wetlands was found to be consistent with the restored area. The supplement amount of water in the three water scenarios of the ponds was The diversion and supplement of water were divided into local water resources, normal supplement, and flood resources. The water supplement amount in each scenario is shown in Figure 4. The change rates of the supplement amount of the total local water resources, as compared to the initially planned scheme in the three scenarios, were −8.68% to 1.08%, −3.35% to 1.98%, and −3.39% to 1.92%, respectively. The change rates of the normal supplement amount, as compared with the initially planned scheme in the three scenarios, were −0.77% to 4.96%, −0.15% to 5.02%, and −0.16% to 3.12%, respectively. The change rates of the supplement amount of flood resources, as compared with the initially planned scheme in the three scenarios, were −51.79% to −40.53%, 1.02% to 3.68%, and 17.57% to 21.36%, respectively.  A total of 12 types of ecological services-namely, food production, raw material production, water supply, carbon sequestration, atmosphere regulation, water regulation and storage, microclimate adjustment, pollution degradation, biodiversity protection, scientific culture, tourism development, and landscape aesthetics-were analyzed in this paper. The comparison of different ecological services in the three scenarios is shown in Figure 5. Fifteen specific ecological services are reflected in the thermal diagram, including fish, crab, reed, water supply, carbon sequestration, oxygen release, water storage and regulation, microclimatic modification, plant fixation, assimilative capacity, biodiversity, scientific culture, tourism development, urban landscape, and nature landscape. In the heat map, the larger the ecological services value, the darker the color. The order of the main ecological services in the low flow year was as follows: food production (27.27-25.53%) > pollution degradation (20.83-20.7%) > microclimate adjustment (13.45-13.47%) > water supply  A total of 12 types of ecological services-namely, food production, raw material production, water supply, carbon sequestration, atmosphere regulation, water regulation and storage, microclimate adjustment, pollution degradation, biodiversity protection, scientific culture, tourism development, and landscape aesthetics-were analyzed in this paper. The comparison of different ecological services in the three scenarios is shown in Figure 5. Fifteen specific ecological services are reflected in the thermal diagram, including fish, crab, reed, water supply, carbon sequestration, oxygen release, water storage and regulation, microclimatic modification, plant fixation, assimilative capacity, biodiversity, scientific culture, tourism development, urban landscape, and nature landscape. In the heat map, the larger the ecological services value, the darker the color. The order of the main ecological services in the low flow year was as follows: food production (27.27-25.53%) > pollution degradation (20.83-20.7%) > microclimate adjustment (13.45-13.47%) > water supply (11.48-11.07%) > water regulation and storage (10.26-11.22%); the order in the normal flow year was as follows: pollution degradation (29.2-28.35%) > food production (19.04-17.75%) > microclimate adjustment (18.4-17.92%) > water regulation and storage (9.14-10.36%) > water supply (8.24-7.72%); and the order in the high flow year was as follows: pollution degradation (30.27-28.19%) > microclimate adjustment (19.03-17.83%) > food production (18.04-17.86%) > water regulation and storage (8.97-10.39%) > water supply (7.8-7.8%).

Comparison Results of the IDCP and IFDCP
This paper aimed to maximize the ecological service value of the western Jilin Province by optimizing the diversion and supplement of water. First, the IDCP was used for optimization, and then the fuzzy programming method was performed based on the IDCP model. The IDCP and IFDCP models from the perspective of the total water surface area, and the total ecological service value optimizations were compared (Figures 6 and 7). For the convenience of analysis, the IDCP and IFDCP model were called Model 1 and Model 2, respectively.

Comparison Results of the IDCP and IFDCP
This paper aimed to maximize the ecological service value of the western Jilin Province by optimizing the diversion and supplement of water. First, the IDCP was used for optimization, and then the fuzzy programming method was performed based on the IDCP model. The IDCP and IFDCP models from the perspective of the total water surface area, and the total ecological service value optimizations were compared (Figures 6 and 7). For the convenience of analysis, the IDCP and IFDCP model were called Model 1 and Model 2, respectively.  Compared to Model 1, the values of interval range of the total area of ponds in Model 2 in the low flow year, normal flow year, and high flow year increased by 15.18%, −14.66%, and −29.49%, respectively, and that of the total ecological service value was increased by 59.39%, −7.46%, and −22.29%, respectively.

Analysis of the Restored Area of Wetlands, Lakes, and Ponds Based on the IFDCP
In the high flow year, the restored water surface area of lakes and ponds was higher than the initially planned scheme with enough floodwater amount. In the normal flow year, the water area met the minimum constraints, but did not reach the initial plan because the water amount was limited. In the low flow year, some regions had to lower the limit of the water surface area in order to meet the allocation of short water resources. The total area of the fishpond in the normal flow year and the high flow year was higher than the initial plan in both the years. In the low flow year, the restored fishpond area of regions 5, 6, 11, and 13 was not less than the initial scheme. The fish pond area of regions 8 and 10 was significantly lower than the initial scheme because these two regions had higher water requirements, whereas the local water resources and normal supplement were relatively low, and the flood resources were significantly lower than the normal flow year and the high flow year. The restored area trends of different scenarios of crab ponds were found to be similar to the fishponds. However, in the low flow year, the difference between the restore crab area in different regions and the initial scheme was small, which meant that the water resources could basically meet the water requirement of the crab pond.
The restored wetland area significantly improved in the normal flow year and high flow year as compared to the low flow year. As the objective of the model was to obtain the highest ecological service value, the wetland that can generate higher ecological services should be supplemented after meeting the requirements of the ponds. Li et al. studied the wetlands in the middle and lower reaches of the Yangtze River, which showed the irreplaceable importance of wetlands [16]. The restored area of reed and marsh wetlands in the normal flow year and the high flow year was higher than the initial scheme, and the restored area of the marsh wetland was relatively higher than that of the reed wetland. However, the results of the low flow year showed completely opposite results-that the restored marsh wetland area decreased significantly. At the same time, only the restored reed wetland area in region 12 was higher than the initial scheme. Water supplement prioritizes the water use of reed wetlands and ponds, and finally the marsh wetland that can produce relatively the highest ecological service value. Therefore, when there is enough water, the restored marsh wetland area will be improved, in order to increase the ecological service value, whereas water cannot be supplemented to the marsh wetland in the situation of water shortage. In the case of the low flow year, the lower bound of the restored marsh wetland area was found to be higher than the upper bound. It was speculated that the constraints of the area were at the lower limit, while there was more water in the high flow year; consequently, more water was supplemented to the marsh wetland.

Analysis of the Optimization of Water Diversion and Supplement Based on the IFDCP
On the whole, the local water resources basically remained unchanged as the amount of flood resources increased, which indicates that the local water resources are used preferentially. The normal supplement could be realized in six regions. The upper and lower bounds of the normal supplement in most of the regions in the three scenarios were basically the same. Among them, the upper bound of the normal supplement in the high flow year of regions 6 and 8 decreased by 100% and 71.51%, respectively, compared with the initial scheme, which indicates that the normal supplement amount will be reduced when the water is sufficient. The upper and lower bounds of the flood resource supplement were found to be lower than the initial scheme in the low flow year, because the flood amount was too small, which was opposite in the high flow year due to the sufficient flood resources. Flood resources were considered as the main form of water supplement in different scenarios. Floods are generated naturally, and often offer significant ecological benefits, such as the deposition of rich and fertile sediments on the land near the river and the supplement of groundwater [17]. The proportion of the use of flood resources gradually increased as the amount of flood increased, whereas that of local resources and normal supplements showed a downward trend. The increase in flood utilization in the normal flow year and the high flow year indicates that the western Jilin Province is short of water resources and cannot meet the water requirement of all functions. Therefore, the effective use of flood for water supplement shows a positive significance for enhancing the ecological service value.

Analysis of the Optimization of the Ecological Service Value Based on the IFDCP
The ecological service value could not meet the planning requirements in the low flow year, whereas that of the normal flow year and high flow year significantly improved after optimization. The proportion of the ecological service value of ponds decreased, whereas that of wetlands, especially marsh wetlands, significantly increased with an increase in the flood resources amount, which further indicates that the main reason for the improvement in the ecological service value was the increased wetland area when water was sufficient. The marsh wetland requires less water than the reed wetland when the area is the same, so water is supplemented to the marsh wetland after meeting the requirement of other areas. Therefore, more change was observed in the ecological service value of the marsh wetland. In one of the cases, the lower bound of the functional areas of the proportion of the ecological service value was found to be higher than the upper bound in some regions. However, this is normal due to differences in parameters.
Food production and pollution degradation contributed nearly half of the ecological services in the low flow year. Food production is produced in ponds, including fish and crab. The service of pollution degradation is produced in wetlands, including plant fixation and assimilative capacity. The proportion of the ecological service value generated by wetlands increased in the normal flow year and the high flow year. Among them, pollution degradation, microclimate adjustment, and food production produced more ecological services. Previous study has proved that the wetland can regulate the surface runoff and purify the water quality, and its function of recharging groundwater is particularly important in arid and the semi-arid areas [18]. In the high flow year, the ecological services generated by wetlands were at nearly half. The wetlands primarily improved the ecological service value by plant fixation, assimilative capacity, and microclimate adjustment when water is sufficient.

Comparison Analysis of the IDCP and IFDCP
Some regions (represented by regions 4, 8, 9, 10, and 15) were found in a stage of water shortage in the low flow year, and the optimization range was small. The change in the trend of upper and lower bounds was the same after the fuzzy method was added, resulting in the interval range of Model 2 being greater than that of Model 1. Adding a fuzzy method will fully consider the fuzzy uncertainty of the minimum value of the water surface area, the functional area, and the total area when water resources can guarantee the basic water requirement. Then the lower and upper bounds of Model 1 were increased and reduced, respectively [19].

Comparison Analysis of Multiple Models Based on the Optimization of the Ecological Service Value
The optimization results of the restored functional area of Model 3 were found within the range of the interval results of Model 2. The optimization results of the total functional area (except crab ponds) of Model 5 were found to be higher than the upper bounds of Model 2 ( Table 4). The optimization results of the most evaluation indicators of Models 3-5 were found within the interval results of Model 2 ( Table 5). The total ecological service values of Models 3 and 4 were found in the range of the interval results of Model 2. The total ecological service value of Model 5 was found to be 0.39% higher than the upper bound of Model 2. Model 5 was optimized based on Model 4. As compared to Model 4, the ecological service (such as fish, crabs, and water supply) value produced by fish and crab ponds of Model 5 was reduced, whereas the ecological service (such as microclimate adjustment, plant fixation, and assimilative capacity) value produced by reed and marsh wetlands was increased. This indicates that Model 5 achieved higher ecological service value by decreasing the water surface area limit. However, Models 3-5 did not fully consider the volatility of the parameters except precipitation, water surface area, and flood resources, and cannot provide a flexible planning solution. In addition, Models 4 and 5 set the probability distribution of the flood inflow scenario, which was impacted by subjective factors and was uncertain for the model. Model 5 decreased the water surface area limit in order to obtain the maximum ecological service value, but it was difficult to apply to the actual situation. In the process of adjusting the water diversion and the supplement plan in the western region of Jilin Province, it is necessary to allocate water resources reasonably within a certain range, according to different situations. In summary, the IFDCP model developed in this paper demonstrates certain feasibility, and at the same time, it is convenient and more flexible to distribute and supplement water resources in the western part of Jilin Province.

Conclusions
In this paper, the IFDCP model was developed to achieve the maximum value of ecological services by optimizing the water diversion and supplement of the western region of Jilin Province. The IFDCP model optimization results showed that when there is enough water, the restored marsh wetland area will be improved to increase the ecological service value, and the effective use of flood for water supplement has a positive significance for enhancing the ecological service value. The optimization results of most evaluation indicators of previous models were found within the interval results of the IFDCP model. However, the previous models did not fully consider the volatility of parameters and cannot provide a flexible solution, and there was uncertainty to the models that is difficult to be applied to the actual situation. The optimized range of total ecological service value can be increased by nearly 10% in an IFDCP model compared with the previous models. In the normal flow year, the decision-making space of the crab pond area increased by nearly 25% compared with previous models, and that of the marsh wetland increased by nearly 3%, which facilitates the flexible planning of relevant functional areas. In conclusion, the IFDCP model was more flexible and practical as compared to the models that were developed previously, which provides a feasible plan for water diversion and supplement.