Hindawi Mathematical Problems in Engineering Volume 2020, Article ID 5726523, 9 pages https://doi.org/10.1155/2020/5726523 Research Article A Study on Evaluating Water Resources System Vulnerability by Reinforced Ordered Weighted Averaging Operator Meiqin Suo ,1 Jing Zhang,1 Lixin He ,1 Qian Zhou,2 and Tengteng Kong1 1School of Water Conservancy and Hydroelectric Power, Hebei University of Engineering, Handan 056038, China 2Huazhong University of Science and Technology, Wuhan 430000, China Correspondence should be addressed to Lixin He; [email protected] Received 20 August 2020; Revised 21 September 2020; Accepted 15 October 2020; Published 21 November 2020 Academic Editor: Huiyan Cheng Copyright © 2020 Meiqin Suo et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Evaluating the vulnerability of a water resources system is a multicriteria decision analysis (MCDA) problem including multiple indictors and different weights. In this study, a reinforced ordered weighted averaging (ROWA) operator is proposed by in- corporating extended ordered weighted average operator (EOWA) and principal component analysis (PCA) to handle the MCDA problem. In ROWA, the weights of indicators are calculated based on component score coefficient and percentage of variance, which makes ROWA avoid the subjective influence of weights provided by different experts. Concretely, the applicability of ROWA is verified by assessing the vulnerability of a water resources system in Handan, China. (e obtained results can not only provide the vulnerable degrees of the studied districts but also denote the trend of water resources system vulnerability in Handan from 2009 to 2018. And the indictor that most influenced the outcome is per capita GDP. Compared with EOWA referred to various indictor weights, the represented ROWA shows good objectivity. Finally, this paper also provides the vulnerability of the water resource system in 2025 based on ROWA for water management in Handan City. 1. Introduction resource system until now. Synthesizing the domestic and research results, the concept of water resources vulnerability With the rapid development of economy, the destruction of was summarized by Zou et al. [6] as follows: the nature and water environment, and the continuous change of global state of the water resources system are affected and destroyed environment, the water resources system has suffered a by the threats and damage from human activities and natural series of water safety problems, such as water shortage, disasters, and it is difficult to restore to the original state and contradiction between supply and demand, and water function after being damaged. (e factors affecting the pollution. (e problems are constantly changing the func- vulnerability of the water resources system contain the tion, structure, and characteristics of the water resources system itself and the stress exerted outside the system (such system directly or indirectly, thus affecting the vulnerability as climate change and human activities). (e influencing of the water resources system. (erefore, it is urgent for factors of the water resources system itself involve its in- hydrologists and disaster scholars to study the vulnerability herent structure, function, and complexity. It is generally of water resources. believed that the more complex the system structure, the Vulnerability is widely used in various fields of academic lower the soil and water loss rate, the stronger the research, such as drought vulnerability [1, 2] and ecological groundwater regeneration capacity, the weaker the vul- vulnerability [3, 4]. Vulnerability is a term commonly used nerability of the system, and on the contrary, the stronger the to describe a weakness or flaw in a system, and it is vul- vulnerability of the system. Considering the influencing nerable to specific threats and harmful events [5]. Although factors mentioned above, it is necessary to apply multi- scholars have different understanding on vulnerability, there criteria decision analysis (MCDA) technology to evaluate the is no uniform definition about vulnerability in the water vulnerability of the water resources system. Fortunately, the 2 Mathematical Problems in Engineering EOWA method [7] as one effectively MCDA tool had been ROWA operator. Afterwards, the results analysis is given widely studied and applied. It considers not only the weight specifically to provide the managers with objectively eval- of the factors affecting the multicriteria decision system, but uated solution for the vulnerability of the water resources also the position of the factors in aggregation process and the system in the past and the future. At last, comparisons weight of the experts. For example, Xiao et al. [8] discussed between ROWA and EOWA are conducted to further il- the problem of ordering qualitative data by using an EOWA lustrate the advantages of the proposed ROWA. operator and the processing of qualitative data in multi- attribute decision-making. Wei [9] put forward a group decision-making method of coal mine safety evaluation 2. Methodology based on the EOWA operator, so as to improve the efficiency 2.1. EOWA. For MCDM problems, two key factors (the of safety management, raise the level of safety management, being evaluated indicators and the weights of indicators) and reduce the cost of safety management. should be ascertained and quantified. However, the second (e thought of EOWA is to transform fuzzy sets into factor is generally provided by experts and denoted in verbal specific values and multiply them by corresponding weight. terms which make the evaluation process more subjective And in the calculation process, order weight is considered and complex. (erefore, this study will reinforce the EOWA because the important degrees of all experts are usually operator by introducing APC to improve the second factors unequal. Due to the addition of ordered weight, the extreme and enhance its applicability in handling MCDM problems. value error is reduced. For example, Zarghami et al. applied Definition and concept on EOWA will be presented as the EOWA operator to group decision-making on water follows. resources projects [10]. However, in the vulnerability as- Xu [7] proposed EOWA based on the ordered weighted sessment of the water resources system, many indicators average (OWA) operator and extended glossary of terms. should be considered objectively to reflect the characteristics (e method is to transform fuzzy sets into specific values from different aspects. However, the indicator weights of and multiply them by corresponding weight, which can be EOWA are determined artificially, which contains a large defined as follows. subjective arbitrariness. It is noted that the principal com- ponent analysis (PCA) can decompose the original multiple n Definition 1. (see [13]). S ⟶ S, if F � F � f(s ; s ; ... ; indicators into independent single indicator and carry out α1 α2 s ) � w s ⊕ w s ⊕ ··· ⊕ w s � s , where F is the total diversified statistics. It can not only make the independent αn 1 β 2 β n βn β 1 2 n single indicator unrelated, avoiding overlapping and cross positive score of a scheme β � Pi�1 wiβi; w � (w1; w2; ... ; between the indicators, but also retain the authenticity of the wn) is a weighted vector associated with EOWA, wi ∈ [ ; ](i N); Pn w � s i original indicator through dimensionality reduction 0 1 ∈ i�1 i 1, and input βi is the th largest el- thought. (us, the multi-indicator problem can be inte- ement in a set of language data (s ; s ; ... ; s ). α1 α2 αn w s grated into a single-indicator form avoiding the subjective i is called ordered weight. βi consists of two parts: randomness of artificial decision-making by using PCA. For indicator weight and indicator value. And indicator weights example, Pan and Xu [11] established a fuzzy comprehensive are not equal to each other in real problems [14]. Based on s evaluation model based on PCA. In which, the evaluation these, βn of EOWA can be obtained as follows: factors were screened by PCA, and the characteristic value of the selected indicators was regarded as the weight, which s � P d ; ( ) βn n n 1 reduced the influence of subjective factors and improved the accuracy of the model. Ren et al. [12] used the PCA to wherePn is the indicator weight and dn is the indicator value. evaluate the integrated performance of different hydrogen (e advantages of EOWA are as follows: (1) it can energy systems and select the best scenario. (erefore, one transform fuzzy sets into specific values; (2) using ordered potential methodology to handling MCDA problems and weights to reduce extreme value error in the calculation s the subjectivity of weights is to incorporate the EOWA and because the important degrees for all inputs βn are generally PCA within a general framework, leading to an integrated unequal. All of these make the calculation results more in assessment method. line with the complexity, spatial, and temporal differences Accordingly, the objective of this study is firstly to and fuzziness situation. propose a reinforced ordered weighted averaging (ROWA) Ordered weight wi in the EOWA operator [7] is obtained operator based on PCA and EOWA, to dispose the MCDA by the minimum variable method [15, 16], and the final problems. (e proposed operator would have the following expression [17] is as follows: advantages: (a) effectively reflecting the importance of dif- 2(2n − 1) − 6(n − 1)(1 − θ) ferent decision levels by order weight in the evaluation w � ; (2) system, (b) avoiding overlap and cross among multiple 1 n(n + 1) indicators, and overcoming the subjective randomness of 6(n − 1)(1 − θ) − 2(n − 2) w � ; (3) different weights by the cumulative contribution rate, and n n(n + 1) (c) determining the main factors affecting the evaluation (n − j) (j − 1) system. And secondly, a case study of assessing the vul- wi � × w1 + × wn; if i ∈ f2; ..