4.1. Bi-Objective Water Model Solutions
Table 4 lists the predicted entire advantages for each end-user of Xiamen city based on the application of the bi-objective pseudo interval T2 linear programming method with different acceptance degrees. The results exhibit that the total profit of water consumption is calculated to be (442,784, 462,602.6, 503,821.3, 522,116.7) × 10
6 CNY with acceptance degree = 0. At acceptance degree = 0.75, which is the most common case for FSs, the total profit is estimated as (483,695.5, 505,357.3, 552,043.6, 572,003.8) × 10
6 CNY for the next 15 years for Xiamen.
Figure 4, which is plotted based on
Table 4, shows that the higher acceptance degrees match the higher system profits, suggesting that the DMs could receive total profits that are dependent on the
a degree. The result data apparently contain four points from Z1 to Z4, which correspond to four points of a single-interval T2 FS. The findings clearly show the advantage in relation to the real-world problem of water systems. The flexibility of the decision process is improved by the use of the interval T2 FS rather than using two interval boundaries. The comparison of the average and standard deviation of the acceptance degrees, which is illustrated in
Figure 5 and
Figure 6, exhibits the reliability and stability of the results of the optimal value. The results also indicate that the profit value can be closer to (491,303.5, 536,161.5) × 10
6 CNY with a lower limit of 470,247.9 × 10
6 CNY and upper limit of 555,563.4 × 10
6 CNY, for example, when the acceptance degree = 0.5. According to the analysis method of the effects of the uncertainty degree, the advantages presented in
Figure 7 show that the lowest and highest uncertain degree that can contribute to an effective solution are less than 4.34% and no more than 8.29%, respectively. Correspondingly, the solutions demonstrate that the interval T2 FSs can really reflect the uncertainties.
4.2. Water Demands of End-Users
Table 5 lists the water supply quantity for industrial, agricultural, and municipal users at different acceptance degrees. The result shows the required water consumption, which is expected to significantly increase because of the rapid economic activities in the three five-year planning periods. From the perspective of the water level, when the water supply is high, there is a fluctuation in the water demand of the information technology industry in both periods 2 and 3. The water demand of the information technology industry is (223.1, 218, 218, 218, 218) × 10
6 cubic meters in the second five-year period, and it remains the same in the third five-year period. The results indicate that the DMs can achieve different optimal solutions by choosing different acceptance degrees according to their risk preference. The group of results indicates that such an industry has certain risk preferences for consuming water, which implies that the information technology factories face higher water treatment costs than other industries. This group of results also clarifies that the water volume remains at 223.1 × 10
6 cubic meters only in the case of zero acceptance degree; it is not constant at other acceptance degrees, including 0.25, 0.5, 0.75, and 1. This trend suggests that this category of industry requires the necessary wastewater treatment to significantly reduce the risk preferences.
When the water level is medium, the results of the petrochemical and biotechnology industries include the results of the interval T2 FSs, which can be dealt with the acceptance degrees by the DMs. The results reveal that there is (230.6, 257.4, 267.8, 278.2, 288.7) × 106 cubic meters of water consumption by the petrochemical industry over the three planning periods, respectively. This indicates that this industry achieves a certain balance by controlling the water quality, water recycling, and wastewater treatment requirements with a relatively medium water supply. By applying a 0.5 acceptance degree, DMs can obtain the optimal solution of 267.8 × 106 cubic meters, which is the common selected result with the fuzzy theory and it largely enhances the flexibility of decision-making. In the biotechnology industry, the water supply is stable in the first period at all acceptance degrees; however, during the second and third planning periods, the demand water is (218.1, 213, 213, 213, 213) × 106 cubic meters. This demand of water implies that the DMs can sufficiently consider the different acceptance degrees when the fuzzy constraints can be violated. It also clearly shows that the starting data of this set of solution is larger than the ending segment data, which implies that the different water volumes correspond to different acceptance degrees. For example, 218.1× 106 cubic meters water is at acceptance degree = zero, which corresponds to a higher system violation risk. At other acceptance degrees, 213 × 106 cubic meters water is allocated to this industry regardless of the period. The lower quantity of water indicates that there may be a water consumption risk owing to the increasing cost of water treatment, which is very good for the local ecosystem as it is saving the water and reducing the waste of water resources.
When the water level is low, the risk of violation of the fuzzy constraints could increase and be affected by the uncertain results of the water supply. The petrochemical, information technology, and machinery industries are individually allocated water supply of (291.2, 302.5, 314.1, 325.5, 337) × 106 cubic meters, (317.1, 328.2, 339.3, 350.4, 361.5) × 106 cubic meters, and (491.2, 496.3, 496.3, 496.3, 496.3) × 106 cubic meters, respectively. Owing to the high profit of the machinery industry in Xiamen city, its water consumption is also gradually increased with a lower risk of constraint violation, and it maintains a maximum water supply during the second and third periods. The FS of the results is mostly obtained from the wastewater treatment cost with water recycling activities, which help improve the local environment. Under the constraints of the local environmental regulations. For example, the treatment rate of recycling water, the risk of water consumption would be particularly taken by the petrochemical and information technology factories, and the balance of profit will increase the usage by the industries.
A comparison of the actual water consumption and planned water supply in the three periods is shown in
Figure 8. The results indicate that the water demand of all the industries at Xiamen city is estimated to be less than the planned water volumes. This confirms that the cost of water treatment, including fresh water and wastewater treatment, is an effective tool for reducing the water supply of factories. This implies that a higher usage of water is associated with more responsibility. The remaining amount of water can be returned for usage by the municipal bodies, which would reduce the daily living cost of the population in this city. In this figure, for example, when the DMs take 0.5 acceptance degree for the entire water system, the water demand by agriculture is obviously higher than the planned water volume, except for the water usage in the first period. The first period of this water model is based on the assumptions of the beginning year. However, in the second five-year period, the water demand increases to the volume of planned water. This is owing to the lower cost of water supply. For agricultural water, individual water treatment and recycling of water are not required. Therefore, the quantity of water that can be supplied to this sector is naturally increased. Moreover, the reduction in the industrial water demand leads to a lower cost of sharing of the excess water. Similar to an industrial user, the municipal water supply is much lower than planned. This is not only caused by the level of natural water but also by the cost of the wastewater treatment. This will encourage citizens in this area to save more water, which will definitely have a positive effect on the population development. However, the results of water supply would be changed with the violation of the constraints. Consequently, the DMs should take more steps to evaluate the system risk and make a practical decision based on the regulation of the local environment. To complete such requirements, it is a remarkable feature of method under different acceptance degrees.
This study also discussed the effect of water shortage on each end-user at different acceptance degrees and water levels. The variations in water shortage are mostly caused by the water quality control, water treatment cost, and water level.
Figure 9 as an example shows that the industrial users contribute the most to water shortage at each water level, particularly at a high-water level. This implies that although the industrial users are high-profit producers, they also encounter a high-water cost, and so, only reduce the water consumption to reduce the costs and increase the profits for each unit. The water that is planned for the industrial users is supplied to the agricultural and municipal users. Therefore, according to the modeling results, agricultural users have the least water in any period or at any acceptance degree. The agricultural users only face a shortage of water in period 1, but have a sufficient supply in periods 2 and 3. For the municipal users, the water shortage is 37 × 10
6 cubic meters and 75 × 10
6 cubic meters, which is common at medium and high water levels. However, at a low water-level, a municipal user is confronted with water shortage. This is because of the high cost of purchasing water from other cities. Additionally, major results of water shortage at the acceptance degree of 0.5 are presented in
Table 6, which includes the water shortage for three types of users: industrial, agricultural, and municipal consumers. Compared with the other results at different acceptance degrees, the main difference is in the supply of water to the industrial users. Specifically, with a higher acceptance degree, a smaller quantity of water is supplied to the industrial users, except the machinery industry, which is accompanied by a large profit of water usage. This scenario is also consistent with the actual requirement of the local area.