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Keywords = stochastic multi-criteria group decision making

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23 pages, 1203 KB  
Article
Selecting Food Loss and Waste Mitigation Technologies Under Preference Uncertainty: An Explainable Multi-Criteria Decision Support Framework
by António Carvalho, João Paulo Moura, Frederico Branco, Carlos Serôdio and Pedro Couto
Sustainability 2026, 18(10), 4735; https://doi.org/10.3390/su18104735 - 9 May 2026
Viewed by 702
Abstract
Food Loss and Waste (FLW) remain major challenges for global food security, environmental sustainability, and economic stability, with nearly one-third of food produced each year being lost or wasted. Although many technologies exist to mitigate FLW, they are often assessed separately, making it [...] Read more.
Food Loss and Waste (FLW) remain major challenges for global food security, environmental sustainability, and economic stability, with nearly one-third of food produced each year being lost or wasted. Although many technologies exist to mitigate FLW, they are often assessed separately, making it difficult for decision-makers to compare options and select solutions suited to specific contexts. This research introduces an explainable decision support system (XDSS) that helps prioritise FLW mitigation strategies while accounting for uncertainty in stakeholder preferences. The proposed framework combines the Best–Worst Method (BWM) with Stochastic Multi-criteria Acceptability Analysis for Group Decision-Making (SMAA-2) to produce transparent and uncertainty-aware rankings. It evaluates one hundred FLW mitigation strategies across five contextual criteria: geographic fit, product category, food supply-chain stage, stakeholder role, and technology type. Rather than producing a single fixed ranking, the system generates probabilistic rank-acceptability profiles that indicate the likelihood of each strategy performing well under different preference conditions. Illustrative scenarios demonstrate that the framework can translate qualitative user preferences into robust prioritisation outcomes, with leading alternatives achieving first-rank-acceptability levels between 62% and 74%. These results indicate that the system can support clearer and more flexible decision-making when preferences are incomplete, inconsistent, or uncertain. Although the current results are based on simulated structured cases, the proposed XDSS provides a transparent methodological foundation for future real-world validation and operational deployment. The framework offers practical value for selecting FLW technologies and for policy planning, contributing to more sustainable food systems and supporting progress toward SDG 12.3. Full article
(This article belongs to the Section Sustainable Food)
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42 pages, 967 KB  
Article
A Stochastic Fractional Fuzzy Tensor Framework for Robust Group Decision-Making in Smart City Renewable Energy Planning
by Muhammad Bilal, A. K. Alzahrani and A. K. Aljahdali
Fractal Fract. 2026, 10(1), 6; https://doi.org/10.3390/fractalfract10010006 - 22 Dec 2025
Cited by 2 | Viewed by 1100
Abstract
Modern smart cities face increasing pressure to invest in sustainable and reliable energy systems while navigating uncertainties arising from fluctuating market conditions, evolving technology landscapes, and diverse expert opinions. Traditional multi-criteria decision-making (MCDM) approaches often fail to fully represent these uncertainties [...] Read more.
Modern smart cities face increasing pressure to invest in sustainable and reliable energy systems while navigating uncertainties arising from fluctuating market conditions, evolving technology landscapes, and diverse expert opinions. Traditional multi-criteria decision-making (MCDM) approaches often fail to fully represent these uncertainties as they typically rely on crisp inputs, lack temporal memory, and do not explicitly account for stochastic variability. To address these limitations, this study introduces a novel Stochastic Fractional Fuzzy Tensor (SFFT)-based Group Decision-Making framework. The proposed approach integrates three dimensions of uncertainty within a unified mathematical structure: fuzzy representation of subjective expert assessments, fractional temporal operators (Caputo derivative, α=0.85) to model the influence of historical evaluations, and stochastic diffusion terms (σ=0.05) to capture real-world volatility. A complete decision algorithm is developed and applied to a realistic smart city renewable energy selection problem involving six alternatives and six criteria evaluated by three experts. The SFFT-based evaluation identified Geothermal Energy as the optimal choice with a score of 0.798, followed by Offshore Wind (0.722) and Waste-to-Hydrogen (0.713). Comparative evaluation against benchmark MCDM methods—TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), VIKOR (VIšekriterijumsko KOmpromisno Rangiranje), and WSM (Weighted Sum Model)—demonstrates that the SFFT approach yields more robust and stable rankings, particularly under uncertainty and model perturbations. Extensive sensitivity analysis confirms high resilience of the top-ranked alternative, with Geothermal retaining the first position in 82.4% of 5000 Monte Carlo simulations under simultaneous variations in weights, memory parameter (α[0.25,0.95]), and noise intensity (σ[0.01,0.10]). This research provides a realistic, mathematically grounded, and decision-maker-friendly tool for strategic planning in uncertain, dynamic urban environments, with strong potential for deployment in wider engineering, management, and policy applications. Full article
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16 pages, 848 KB  
Article
A Group-Decision-Making Framework for Evaluating Urban Flood Resilience: A Case Study in Yangtze River
by Huagui Zhu and Fan Liu
Sustainability 2021, 13(2), 665; https://doi.org/10.3390/su13020665 - 12 Jan 2021
Cited by 33 | Viewed by 4538
Abstract
Floods are among the most common and destructive natural disasters confronted by cities and are further aggravated by rapid climate change and increasing urbanization, posing a great challenge to flood risk management. To cope with uncertainty, there is a need to move towards [...] Read more.
Floods are among the most common and destructive natural disasters confronted by cities and are further aggravated by rapid climate change and increasing urbanization, posing a great challenge to flood risk management. To cope with uncertainty, there is a need to move towards approaches to managing flood risk by taking resilience into consideration. While the evaluation of urban flood resilience has gained much attention in recent decades, studies on quantitative measurement using multiple criteria decision making (MCDM) approaches are rare. In addition, the results determined by different MCDM methods may exhibit considerable variability. It is an intractable task to gather a group consensus from these methods. In this regard, in this paper, we propose a group-decision-making framework for measuring urban resilience to flooding, combining three stages, which are (i) normalizing the data, (ii) weighting the criteria and (iii) aggregating the results. Four objective MCDM methods—i.e., the variation coefficient method, Shannon weighting method, CRITIC and ideal point method—are proposed and treated as reliable methods. A stochastic multi criteria acceptability analysis is adopted to integrate those results into a composite resilience index. The proposed methodology is applied to the resilience evaluation problem of 41 cities in the Yangtze River basin, and the results are compared with those obtained with the four MCDM methods. It is demonstrated that our method considers all possible preferences among the results provided by various MCDM methods and is thus more robust and acceptable. Full article
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17 pages, 869 KB  
Article
Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory
by Yuanxiang Dong, Chenjing Hou, Yuchen Pan and Ke Gong
Symmetry 2019, 11(9), 1085; https://doi.org/10.3390/sym11091085 - 29 Aug 2019
Cited by 5 | Viewed by 3329
Abstract
To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the [...] Read more.
To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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18 pages, 2531 KB  
Article
Risk Assessment and Decision-Making Based on Mean-CVaR-Entropy for Flood Control Operation of Large Scale Reservoirs
by Quansen Wang, Jianzhong Zhou, Kangdi Huang, Ling Dai, Gang Zha, Lu Chen and Hui Qin
Water 2019, 11(4), 649; https://doi.org/10.3390/w11040649 - 28 Mar 2019
Cited by 13 | Viewed by 3828
Abstract
The risk inevitably exists in the process of flood control operation and decision-making of reservoir group, due to the hydrologic and hydraulic uncertain factors. In this study different stochastic simulation methods were applied to simulate these uncertainties in multi-reservoir flood control operation, and [...] Read more.
The risk inevitably exists in the process of flood control operation and decision-making of reservoir group, due to the hydrologic and hydraulic uncertain factors. In this study different stochastic simulation methods were applied to simulate these uncertainties in multi-reservoir flood control operation, and the risk caused by different uncertainties was evaluated from the mean value, extreme value and discrete degree of reservoir occupied storage capacity under uncertain conditions. In order to solve the conflict between risk assessment indexes and evaluate the comprehensive risk of different reservoirs in flood control operation schemes, the subjective weight and objective weight were used to construct the comprehensive risk assessment index, and the improved Mahalanobis distance TOPSIS method was used to select the optimal flood control operation scheme. The proposed method was applied to the flood control operation system in the mainstream and its tributaries of upper reaches of the Yangtze River basin, and 14 cascade reservoirs were selected as a case study. The results indicate that proposed method can evaluate the risk of multi-reservoir flood control operation from all perspectives and provide a new method for multi-criteria decision-making of reservoir flood control operation, and it breaks the limitation of the traditional risk analysis method which only evaluated by risk rate and cannot evaluate the risk of the multi-reservoir flood control operation system. Full article
(This article belongs to the Section Water Resources Management, Policy and Governance)
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20 pages, 355 KB  
Article
Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems
by Dheeraj Kumar Joshi, Ismat Beg and Sanjay Kumar
Mathematics 2018, 6(4), 47; https://doi.org/10.3390/math6040047 - 26 Mar 2018
Cited by 30 | Viewed by 6050
Abstract
Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element (HFLE) and define hesitant probabilistic fuzzy linguistic set (HPFLS) for ill [...] Read more.
Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element (HFLE) and define hesitant probabilistic fuzzy linguistic set (HPFLS) for ill structured and complex decision making problem. HPFLS provides a single framework where both stochastic and non-stochastic uncertainties can be efficiently handled along with hesitation. We have also proposed expected mean, variance, score and accuracy function and basic operations for HPFLS. Weighted and ordered weighted aggregation operators for HPFLS are also defined in the present study for its applications in multi-criteria group decision making (MCGDM) problems. We propose a MCGDM method with HPFL information which is illustrated by an example. A real case study is also taken in the present study to rank State Bank of India, InfoTech Enterprises, I.T.C., H.D.F.C. Bank, Tata Steel, Tata Motors and Bajaj Finance using real data. Proposed HPFLS-based MCGDM method is also compared with two HFL-based decision making methods. Full article
(This article belongs to the Special Issue Fuzzy Mathematics)
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