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Attribute weighting is a task of paramount relevance in multi-attribute decision-making (MADM). Over the years, different approaches have been developed to face this problem. Despite the effort of the community, there is a lack of consensus on which method is the most suitable one for a given problem instance. This paper is the second part of a two-part survey on attribute weighting methods in MADM scenarios. The first part introduced a categorization in five classes while focusing on explicit weighting methods. The current paper addresses implicit and hybrid approaches. A total of 20 methods are analyzed in order to identify their strengths and limitations. Toward the end, we discuss possible alternatives to address the detected drawbacks, thus paving the road for further research directions. The implicit weighting with additional information category resulted in the most coherent approach to give effective solutions. Consequently, we encourage the development of future methods with additional preference information.

Attribute weighting is a key aspect when modeling multi-attribute decision analysis problems. Despite the large number of proposals reported in the literature, reaching a consensus on the most convenient method for a certain scenario is difficult, if not impossible. As a first contribution of this paper, we propose a categorization of existing methodologies, which goes beyond the current taxonomy (subjective, objective, hybrid). As a second contribution, supported by the new categorization, we survey and critically discuss the explicit weighting methods (which are closely related to the subjective ones). The critical discussion allows evaluating how much a solution can deviate from the expected one if no foresight is taken. As a final contribution, we summarize the main drawbacks from a global perspective and propose some insights to correct them. Such a discussion attempts to improve the reliability of decision support systems involving human experts.

The entropy-weighting method (EWM) and variation coefficient method (VCM) are two typical diversity-based weighting methods, which are widely used in risk assessment and decision-making for natural hazards. However, for the attributes with a specific range of values (RV), the weights calculated by EWM and VCM (abbreviated as WE and WV) may be irrational. To solve this problem, a new indicator representing the dipartite degree is proposed, which is called the coefficient of dipartite degree (CDD), and the corresponding weighting method is called the dipartite coefficient method (DCM). Firstly, based on a large amount of statistical data, a comparison between the EWM and VCM is carried out. It is found that there is a strong correlation between the weights calculated by the EWM and VCM (abbreviated as WE and WV); however, in some cases the difference between WE and WV is big. Especially when the diversity of attributes is high, WE may be much larger than WV. Then, a comparison of the DCM, EWM and VCM is carried out based on two case studies. The results indicate that DCM is preferred for determining the weights of the attributes with a specific RV, and if the values of attributes are large enough, the EWM and VCM are both available. The EWM is more suitable for distinguishing the alternatives, but prudence is required when the diversity of an attribute is high. Finally, the applications of the diversity-based weighting method in natural hazards are discussed.

Over the past few years, numerous deep learning-based methods have been proposed for incomplete multi-view clustering. However, these approaches overlook two crucial issues. First, they focus solely on the global information contained in the latent representations derived from deep networks, neglecting the importance of local focal points. Second, while leveraging consistent or complementary inter-view information for cross-view learning, they disregard the intrinsic relationships among different samples within the same view. To address these concerns, this manuscript presents an original approach: incomplete multi-view clustering based on self-attention networks and feature reconstruction (SNFR). Specifically, SNFR initially employs self-attention networks to emphasize the pivotal information within views, aiming to reduce the inter-view reconstruction loss. Subsequently, an improved entropy weighting method is applied to reconstruct the feature relationships among the diverse samples within the same view, thereby facilitating consistent cross-view information learning. Our proposed method is evaluated on six widely used multi-view datasets through extensive experiments, highlighting its remarkable superiority over the alternative approaches in terms of clustering performance

In multi-criteria decision-making (MCDM) environments characterized by uncertainty and data irregularities, the reliability of weighting methods becomes critical for ensuring robust and accurate decisions. This study introduces a novel hybrid objective weighting method—IQRBOW-E (Interquartile Range-Based Objective Weighting with Entropy)—which dynamically combines the statistical robustness of the IQRBOW method with the information sensitivity of Entropy through a tunable parameter β. The method allows decision-makers to flexibly control the trade-off between robustness and information contribution, enhancing the adaptability of decision support systems. A comprehensive experimental design involving ten simulation scenarios was implemented, in which the number of criteria, alternatives, and outlier ratios were varied. The IQRBOW-E method was integrated into the VIKOR framework and evaluated through average Q values, stability ratios, SRD scores, and the Friedman test. The results indicate that the proposed hybrid approach achieves superior decision stability and performance, particularly in data environments with increasing outlier contamination. Optimal β values were shown to shift systematically depending on data conditions, highlighting the model’s sensitivity and adaptability. This study not only advances the methodological landscape of MCDM by introducing a parameterized hybrid weighting model but also contributes a robust and generalizable weighting infrastructure for modern decision-making under uncertainty.

Under the background of new-type urbanization and rural revitalization strategy, how to promote the development of urban–rural integration has become an important issue in today’s society. This paper designed a new evaluation mechanism for the development level of urban–rural integration. Specifically, a three-level evaluation index system of urban–rural integration development level was established from four aspects: spatial integration, economic integration, social integration and living environment integration. By combining the entropy weight method with the ranking method, a combination weighting method was proposed to determine the weight of each index in the index system. Furthermore, an improved TOPSIS method based on relative entropy and grey relational degree was proposed to evaluate the development level of urban–rural integration, which considering proximity from the perspectives of distance and shape and solving the problem that some situations cannot be compared through the original model. Then, the established evaluation mechanism was applied to make an empirical analysis for evaluating the development level of urban–rural integration in Hubei Province, China. Cluster analysis and obstacle factor analysis were used to further analyze the evaluation results. Finally, according to the evaluation results, some effective countermeasures and policy implications were provided to improve the development level of urban–rural integration in Hubei Province.

Liquid lifting is a low-cost, straightforward, and efficient measure for stabilizing production, achieved by adjusting liquid production to reduce bottom-hole flow pressure, thereby optimizing reservoir development and increasing recovery rates. However, traditional research methods for liquid lifting no longer meet the demands of contemporary oilfield big data applications. Particularly in the selection of target wells for liquid lifting, manual screening based on chart methods faces challenges such as low efficiency, high workload, and poor generalization capabilities. This study focuses on the oil wells in the high water cut phase of the SL oilfield in China and proposes a novel data-driven approach to predict the liquid lifting effects of oil wells. This method forecasts the effect of liquid lifting measures based on dynamic and static production data before the implementation of liquid lifting measures, facilitating intelligent selection of oil wells for liquid lifting measures. Firstly, each evaluation metric is assigned weights by utilizing the Coefficient of Variation-G1 Hybrid Cross-Weighting method. The comprehensive evaluation score is obtained through a weighted sum. Subsequently, the self-organizing map (SOM) clustering method is applied to categorize the oil well liquid lifting effects into four classes (A, B, C, D), representing different levels of effect. Additionally, a learning sample dataset is constructed by selecting multidimensional time-series features before liquid lifting. The oil well liquid lifting effect classification model is established using the Bi-LSTM sequence-to-label deep learning algorithm. Comprehensive testing validates the superior performance of the model, especially with classification accuracies of 0.96 and 0.83 on the training and testing sets, respectively. These results outperform other classification models such as LSTM, XGBoost, and SVM, providing an effective tool for intelligent oil well selection in liquid lifting measures.

City sustainability means a balance among economy, society, and environment in the rapid urbanization process. Effective assessment of city sustainability could guide a city to develop in the desired direction. Northeastern China was one of the forefronts of China’s reform and opening up, but now it has become a “sore point” in national development. Liaoning province plays a crucial role in the process of realizing the revitalization of Northeastern China. This paper investigated the sustainability performances of cities in Liaoning by following the process of multi-criteria decision making. A novel weighting method was proposed based on Synergetics that considers the interrelationship among sustainability criteria. The results showed that the sustainability level of Liaoning was not ideal, with only two cities having sustainability performances over 0.55. The cities located in the Middle region had a higher sustainability level than those in the West and East regions. Moreover, the performances on the three dimensions were uncoordinated. The salary of employed staff and disposal income were the two important factors on sustainable development. The forecasting analysis showed that the sustainability level of the cities will develop at a rapid pace in the future. Finally, we put forward targeted suggestions for sustainable development in Liaoning province.

PurposeThis paper proposes a new multi-criteria decision-making method, called the vital-immaterial-mediocre method (VIMM), to determine the weight of multiple conflicting and subjective criteria in a decision-making problem.Design/methodology/approachThe novel method utilizes pairwise comparisons, vector-based procedures and a scoring approach to determine weights of criteria. The VIMM compares alternatives by the three crucial components, namely the vital, immaterial and mediocre criteria. The vital criterion has the largest effect on the final results, followed by the mediocre criterion and then the immaterial criterion, which is the least impactful on the prioritization of alternatives. VIMM is developed in two forms where the first scenario is designed to solve one-goal decision-making problems, while the second scenario embraces multiple goals.FindingsTo validate the method’s performance and applicability, VIMM is applied to a problem of sustainable supplier selection. Comparisons between VIMM, analytic hierarchy process (AHP) and best-worst method (BWM) reveal that VIMM significantly requires fewer comparisons. Moreover, VIMM works well with both fractional and integer numbers in its comparison procedures.Research limitations/implicationsAs an implication for research, we have added the development of the VIMM under fuzzy and grey environments as the direction for optimization of the method.Practical implicationsAs managerial implications, VIMM not only provides less complex process for the evaluation of the criteria in the managerial decision-making process, but it also generates consistent results, which make VIMM a reliable tool to apply to a large number of potential decision-making problems.Originality/valueAs a novel subjective weighting method, there exist five major values that VIMM brings over AHP and BWM methods: VIMM requires fewer comparisons compared with AHP and BWM; it is not sensitive to the number of criteria; as a goal-oriented method, it exclusively takes the decision-making goals into account; it keeps the validity and reliability of the Decision-Makers’ (DMs’) opinions and works well with integer and fractional numbers.

The division of the flood season is of great significance for the precise operation of water conservancy projects, flood control and disaster reduction, and the rational allocation of water resources, alleviating the contradiction of the uneven spatial and temporal distribution of water resources. The single weighting method can only determine the weight of the flood season division indicators from a certain perspective and cannot comprehensively reflect the time-series attributes of the indicators. This study proposes a Flood Season Division Model based on the Goose Optimization Algorithm and Minimum Deviation Combined Weighting (FSDGOAMDCW). The model uses the Goose Optimization Algorithm (GOA) to solve the Minimum Deviation Combination model, integrating weights from two subjective methods (Expert Scoring and G1) and three objective methods (Entropy Weight, CV, and CRITIC). Combined with the Set Pair Analysis Method (SPAM), it realizes comprehensive flood season division. Based on daily precipitation data of the Nandujiang River (1961–2022), the study determines its flood season from 1 May to 30 October. Comparisons show that: ① GOA converges faster than the Genetic Algorithm, stabilizing at T = 5 and achieving full convergence at T = 24; and ② The model’s division results have the smallest Intra-Class Differences, avoiding indistinguishability between flood and non-flood seasons under special conditions. This research aims to support flood season division studies in tropical islands.