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In multi-attribute decision making (MADM), complex situations often arise where decision attributes are interval-valued hesitant fuzzy numbers (IVHFNs) and the attributes are interrelated. Traditional decision-making methods may be ineffective in handling such cases, highlighting the practical importance of seeking more effective approaches. Therefore, finding a more effective decision-making approach has important practical significance. By combining the theories of Archimedean S-norms and T-norms, we innovatively propose a multi-attribute decision-making method based on the generalized interval-valued hesitant fuzzy weighted Heronian mean (GIVHFWHM) operator to address the aforementioned issues. Initially, based on the operational laws of IVHFNs and the Heronian mean (HM) operator, we introduce the generalized interval-valued hesitant fuzzy Heronian mean (GIVHFHM) operator and the GIVHFWHM operator. We then examine properties of the GIVHFHM operator, including permutation invariance, idempotency, monotonicity, boundedness, and parameter symmetry. A multi-attribute decision-making model is constructed based on the GIVHFWHM operator. Finally, we validate the proposed model through numerical experiments in MADM. The results demonstrate that the new decision-making method, based on the GIVHFWHM operator, is feasible and effective in handling multi-attribute decision problems involving IVHFNs with interdependent attributes. This approach provides a novel perspective and method for solving MADM problems under interval-valued hesitant fuzzy conditions with interdependent attributes. It enriches the theoretical framework of multi-attribute hesitant decision models and expands the application of the Heronian mean operator within interval-valued hesitant fuzzy environments. This methodology assists decision makers in making more accurate decisions within complex decision-making contexts, enhancing both the scientific rigor and reliability of decision-making processes. [ABSTRACT FROM AUTHOR]

Introduction: An innovative methodology is proposed to delve into the pivotal role of regional distribution networks (RDNs) in fostering low-carbon development. Methods: The methodology first constructs an evaluation framework encompassing various dimensions and then integrates spherical fuzzy sets (SFSs) with the best-worst method (BWM), enabling the precise calculation of indicator weight parameters. Subsequently, we employ the measurement of alternatives and ranking according to compromise solution (MARCOS) with SFSs to process and synthesize decision making information. Results: Take the Shanghai region as an example, results show that C4 has the highest performance and C10 has the lowest. Discussion: In conclusion, this research presents a significant step forward in understanding the importance of RDNs in promoting low-carbon development and offers a practical approach for decision-makers to assess and enhance the performance of RDNs. [ABSTRACT FROM AUTHOR]

Quadripartition neutrosophic number is an extension of the neutrosophic set constructed for modeling situations specifically with incomplete, indeterminate, and inconsistent information. In this paper, Quadripartition Neutrosophic Weighted Hamacher Averaging Aggregative operator and Quadripartition Neutrosophic Weighted Hamacher Geometric Aggregative operator are introduced. Hamacher aggregation operators are the extension of the algebraic aggregation operators and Einstein aggregation operators, which are more general and flexible. Some essential properties such as idempotency, commutativity, monotonicity, and boundedness properties have been investigated. A new MADM strategy is developed using the proposed operators. The entropy function is used to calculate the weights of the attributes in aggregating the decision maker's preferences. An MADM problem of COVID-19 patient's oxygen supply is solved to demonstrate the process. In addition, a comparison is made to ensure that the proposed strategies are consistent and superior. [ABSTRACT FROM AUTHOR]

Copyright of Environmental & Social Management Journal / Revista de Gestão Social e Ambiental is the property of Environmental & Social Management Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the traditional decision-making process for product form design, designers and experts often prioritize schemes based on their own knowledge and experience. This approach can lead to an oversight of user preferences, ultimately affecting decision outcomes. In contrast, crowd-intelligence-driven, multi-attribute decision-making for product form design in the cloud environment builds upon traditional approaches by leveraging the vast and diverse expertise of individuals on cloud platforms, engaging participants from various fields and roles in the decision-making process to enhance comprehensiveness and accuracy. To address the issue of a single decision-maker and limited user participation in the decision-making process for product form design schemes in the cloud environment, a multi-attribute decision-making method integrating expert knowledge and user preferences is proposed. This method aims to select a product form design scheme that optimally balances expert and user satisfaction. Initially, the Pythagorean Hesitant Fuzzy Set (PHFS) is used to quantify qualitative product attributes and to establish a comprehensive multi-attribute evaluation system. In the aspect of expert decision-making, a gray correlation coefficient decision matrix based on expert knowledge is established and the overall score of the base alternative is calculated by the ViseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method and the Improved Osculating Value method. In terms of user decision-making, weights are determined by calculating the similarity between user evaluation matrices, and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to calculate scores for product form designs based on user preferences. Ultimately, optimal selection is achieved by aggregating the aforementioned expert evaluation values and user preference values. The method's effectiveness and feasibility are confirmed through a case study of coffee machine product form design schemes. [ABSTRACT FROM AUTHOR]

In this paper, four kinds of interval-valued intuitionistic fuzzy β covering rough set models are proposed on a new ẞ covering neighborhood system, which can be used to effectively deal with multi-attribute decision making with interval-valued intuitionistic fuzzy information. Firstly, based on the interval-valued intuitionistic fuzzy β covering of the discourse domain, two new neighborhood systems are introduced and four different types of intuitionistic fuzzy β covering rough sets are constructed to extend the application range of the existing model. Secondly, the mathematical properties of each model are studied deeply, and the correlation between the four models is established, which provides a theoretical basis for the study of fuzzy β covering rough sets. Finally, in order to solve the multi-attribute decision making problem with interval-valued intuitionistic fuzzy information, a decision algorithm is designed and an application example is analyzed. By comparing with other decision making methods, the feasibility and effectiveness of interval-valued intuitionistic fuzzy β covering rough sets are demonstrated. The research results of this paper have a certain reference and guiding significance for complex fuzzy information decision-making, and provide a new way and method for solving multi-attribute decision-making problems. [ABSTRACT FROM AUTHOR]

Faced with rapidly rising energy demand in industrialised societies and widespread global concern, countries are actively promoting the transition from conventional to renewable energy systems. The goal is to invest in renewable energy in the most efficient way to meet rising energy demand and reduce the challenges posed by climate change. However, decision makers must carefully weigh various factors when selecting the most appropriate renewable energy investment projects. This paper presents a novel method for Multi-Attribute Decision Making(MADM) that uses the Bipolar Complex Fuzzy(BCF) to convey the vagueness and uncertainty of decision makers, so that the result obtained better reflects the actual scenario and the subjective biases of decision makers. We defined BCF Einstein Weighted Averaging (BCFEWA) operator and BCF Einstein Ordered Weighted Averaging (BCFEOWA) operator to aggregate evaluation information. Then we discussed some properties of the proposed aggregation operators. Additionally, we present an integrated MADM technique grounded in the BCF framework that combines the CRiteria Importance Through Intercriteria Correlation (CRITIC) and ELECTRE III methods. Specifically, the CRITIC method determines attribute weights, and the ELECTRE III method ranking the alternatives to determine the best renewable energy investment projects. After analysing the results and comparisons, it can be inferred that the suggested methodology offers an effective evaluation process. [ABSTRACT FROM AUTHOR]

This study presents the results of a numerical analysis of the response of Domex 700 and Dormex 1100 steel plates with varying geometries, combined with several different parameters such as a thickness of up to 6 mm and a trinitrotoluene (TNT) mass. Using ABAQUS software, finite-element analysis was run to examine the structural response ability of the steel plates to explosions. In terms of deformation and energy dissipation, the results showed a large differentiation. A sensitivity analysis was used to examine each simulation result in terms of the structural response performance to explosions and identify the variables that had the greatest impact on variations in the thickness, material, geometry, and TNT mass. The best numerical simulation results were found using the multi-attribute decision-making (MADM) approach. Annotations are utilized to assist in identifying the various modifications made during testing. Annotations LXXI to LVIII achieved the lowest value of 6.176 × 10−09, signifying the best results according to calculations made using the MADM approach. This is evidenced by the structural events, demonstrating that the deformation, von Mises stress, and energy dissipation in the circular plate structure were not significantly impacted by the explosion. The variables that most significantly affect variations in deformation, von Mises stress, and dissipated energy – variables that significantly impact the structural response to explosions – are identified through the sensitivity analysis approach. The results of this research can be used to optimize the structural response performance of circular plates.

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed. [ABSTRACT FROM AUTHOR]

This paper proposes a linear consensus protocol QuickBFT based on Vague sets and multi-attribute decision-making methods. QuickBFT simplifies the communication process based on the HotStuff protocol, reduces the four-stage communication to three-stage communication, and reduces the consensus delay. Furthermore, we introduce the Vague set and multi-attribute decision-making theory into the consensus protocol and propose a new leader node selection algorithm, which can prevent Byzantine nodes from becoming leader nodes, thereby improving the protocol performance when the leader node is attacked. Experimental results show that the throughput of QuickBFT is slightly higher than that of the HotStuff protocol without Byzantine nodes, and the consensus delay is reduced by 20%. In the presence of Byzantine nodes, the throughput of QuickBFT is increased by 80% compared with the HotStuff protocol, and the consensus delay is reduced by 60%. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper aims at automatic route choice in wargame deduction, that is, using computer algorithms to mimic the route choice of human players. Route choice is the process by which a player of a game chooses the optimal route from a set of candidate routes. Essentially, it can be viewed as a multi-attribute decision making problem. However, due to the uncertain and dynamic decision making environment in wargaming, the existing decision making theory and methods face some challenges in addressing such problems. We summarize these challenges in two aspects. On the one hand, from a psychological point of view, the process of route choice by a human player is a dynamic decision making process. However, most of the multi-attribute decision making methods widely used today were developed under static conditions and do not accurately describe the decision making behaviors of individuals in dynamic and real-world settings. On the other hand, in the real dynamic decision making environment of wargaming, there is a large amount of ambiguous and uncertain information. How to imitate human thinking to quantify the information is crucial for making scientific decisions and for automating decision making. Based on the above two aspects of the analysis, in this paper, we first construct a fuzzy dynamic route choice model of wargame. The model simulates the decision making process of humans from two stages of "information preprocessing" and "information processing". Then we propose a fuzzy dynamic route choice algorithm of wargame. Furthermore, the model is applied to a practical case of route choice of wargame, and the effectiveness and advantages of the model are illustrated through a comparative analysis. Finally, the model is further quantitated and analyzed in combination with the actual case, and the approximation of the model to human decision making psychology is illustrated from both a simulation and a mathematical justification perspective. These results demonstrate that the proposed model can not only handle a large amount of fuzzy and uncertain information, but also simulate the decision making psychology of wargame players. This research result is expected to provide a new effective method for automatic route choice in wargame simulations. [ABSTRACT FROM AUTHOR]

IntroductionAn innovative methodology is proposed to delve into the pivotal role of regional distribution networks (RDNs) in fostering low-carbon development.MethodsThe methodology first constructs an evaluation framework encompassing various dimensions and then integrates spherical fuzzy sets (SFSs) with the best-worst method (BWM), enabling the precise calculation of indicator weight parameters. Subsequently, we employ the measurement of alternatives and ranking according to compromise solution (MARCOS) with SFSs to process and synthesize decision making information.ResultsTake the Shanghai region as an example, results show that C4 has the highest performance and C10 has the lowest.DiscussionIn conclusion, this research presents a significant step forward in understanding the importance of RDNs in promoting low-carbon development and offers a practical approach for decision-makers to assess and enhance the performance of RDNs.

Abstract Actual decision making problems are often based on the company decision maker’s behavior factors, such as risk attitude, subjective preference, etc. Regret theory can well express the behavior of the decision maker. In this pursuit, a novel decision making method was developed, based on the regret theory for the multi-attribute decision making problem, in which attribute values were expressed by spherical fuzzy numbers. Distance measurement not only has extensive applications in fields such as pattern recognition and image processing, but also plays an important role in the research of fuzzy decision theory. The existing distance measures of spherical fuzzy set either have special cases of anti-intuition or are more complex in calculation, so finding suitable distance measures is also an important research topic in the decision-making theory of spherical fuzzy set. For this reason, we first establish a new distance of spherical fuzzy sets based on Hellinger distance of probability distribution. A decision maker’s perception utility value function is proposed using the new distance formula, which is used to measure the regretful and rejoice value. Then we establish an optimization model for solving the attribute weights, when the information of attribute weight was partially known. Subsequently, the comprehensive perceived utility values were utilized to rank the order of the alternatives. Finally, a numerical example of assessment of logistics providers is used to show that the new decision making method is effective and feasible.

With the existence of several conventional and advanced building thermal energy demand forecast models to improve the energy efficiency of buildings, it is hard to find an appropriate, convenient, and efficient model. Evaluations based on statistical indexes (MAE, RMSE, MAPE, etc.) that characterize the accuracy of the forecasts do not help in the identification of the efficient building thermal energy demand forecast tool since they do not reflect the efforts entailed in implementation of the forecast model, i.e., data collection to production/use phase. Hence, this work presents a Gini Index based Measurement of Alternatives and Ranking according to COmpromise Solution (GI-MARCOS), a hybrid Multi Attribute Decision Making (MADM) approach for the identification of the most efficient building energy demand forecast tool. GI-MARCOS employs (i) GI based objective weight method: assigns meaningful objective weights to the attributes in four phases (1: pre-processing, 2: implementation, 3: post-processing, and 4: use phase) thereby avoiding unnecessary biases in the expert's opinion on weights and applicable to domains where there is a lack of domain expertise, and (ii) MARCOS: provides a robust and reliable ranking of alternatives in a dynamic environment. A case study with three alternatives evaluated over three to six attributes in four phases of implementation (pre-processing, implementation, post-processing and use) reveals that the use of GI-MARCOS improved the accuracy of alternatives MLR and BM by 6% and 13%, respectively. Moreover, additional validations state that (i) MLR performs best in Phase 1 and 2, while ANN performs best in Phase 3 and 4 with BM providing a mediocre performance in all four phases, (ii) sensitivity analysis: provides robust ranking with interchange of weights across phases and attributes, and (iii) rank correlation: ranks produce by GI-MARCOS has a high correlation with GRA (0.999), COPRAS (0.9786), and ARAS (0.9775).

Abstract To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making.

Actual decision making problems are often based on the company decision maker's behavior factors, such as risk attitude, subjective preference, etc. Regret theory can well express the behavior of the decision maker. In this pursuit, a novel decision making method was developed, based on the regret theory for the multi-attribute decision making problem, in which attribute values were expressed by spherical fuzzy numbers. Distance measurement not only has extensive applications in fields such as pattern recognition and image processing, but also plays an important role in the research of fuzzy decision theory. The existing distance measures of spherical fuzzy set either have special cases of anti-intuition or are more complex in calculation, so finding suitable distance measures is also an important research topic in the decision-making theory of spherical fuzzy set. For this reason, we first establish a new distance of spherical fuzzy sets based on Hellinger distance of probability distribution. A decision maker's perception utility value function is proposed using the new distance formula, which is used to measure the regretful and rejoice value. Then we establish an optimization model for solving the attribute weights, when the information of attribute weight was partially known. Subsequently, the comprehensive perceived utility values were utilized to rank the order of the alternatives. Finally, a numerical example of assessment of logistics providers is used to show that the new decision making method is effective and feasible. [ABSTRACT FROM AUTHOR]

For multi-attribute decision-making problems with decision information as picture fuzzy, this paper firstly defines the assignment of the degree of refusal membership with parameters based on the limitations of existing picture fuzzy distances. It also proposes a picture fuzzy distance that reflects decision-makers' risk preferences by combining consistency concepts. Through a numerical example, the new picture fuzzy distance is compared and analyzed with existing picture fuzzy distances to verify its superiority. Secondly, for attribute weights, this paper adopts the combination weighting method of game theory to combine the objective weights determined by entropy weighting with the subjective weights given by decisionmakers. On this basis, the new picture fuzzy distance is extended to evaluation based on distance from average solution(EDAS)method, and the weighted sum of positive and negative distances between each scheme and the average scheme is calculated using the new distance, resulting in comprehensive scores. Finally, numerical examples are used to verify the applicability and effectiveness of the proposed decision-making method. Sensitivity and comparative analysis results show that decisionmakers can adjust the parameter values according to their risk preferences to meet different decision-making needs. The method is more general and flexible compared to other existing decision-making methods, and the ranking results are more reasonable. [ABSTRACT FROM AUTHOR]

With the existence of several conventional and advanced building thermal energy demand forecast models to improve the energy efficiency of buildings, it is hard to find an appropriate, convenient, and efficient model. Evaluations based on statistical indexes (MAE, RMSE, MAPE, etc.) that characterize the accuracy of the forecasts do not help in the identification of the efficient building thermal energy demand forecast tool since they do not reflect the efforts entailed in implementation of the forecast model, i.e., data collection to production/use phase. Hence, this work presents a Gini Index based Measurement of Alternatives and Ranking according to COmpromise Solution (GI-MARCOS), a hybrid Multi Attribute Decision Making (MADM) approach for the identification of the most efficient building energy demand forecast tool. GI-MARCOS employs (i) GI based objective weight method: assigns meaningful objective weights to the attributes in four phases (1: pre-processing, 2: implementation, 3: post-processing, and 4: use phase) thereby avoiding unnecessary biases in the expert's opinion on weights and applicable to domains where there is a lack of domain expertise, and (ii) MARCOS: provides a robust and reliable ranking of alternatives in a dynamic environment. A case study with three alternatives evaluated over three to six attributes in four phases of implementation (pre-processing, implementation, post-processing and use) reveals that the use of GI-MARCOS improved the accuracy of alternatives MLR and BM by 6% and 13%, respectively. Moreover, additional validations state that (i) MLR performs best in Phase 1 and 2, while ANN performs best in Phase 3 and 4 with BM providing a mediocre performance in all four phases, (ii) sensitivity analysis: provides robust ranking with interchange of weights across phases and attributes, and (iii) rank correlation: ranks produce by GI-MARCOS has a high correlation with GRA (0.999), COPRAS (0.9786), and ARAS (0.9775). [ABSTRACT FROM AUTHOR]

Due to the diversity and complexity of the actual data distribution, the traditional neighborhood classifier (NEC) is weak in adapting to the global data and has low utilization of local information, which leads to the degradation of the classifier's effectiveness. To adapt NEC to the differences of different dimensions in data distribution, this paper defines attribute sensitivity and improves the purity of neighborhood information granules by weighted distance. To improve the resolution of local information, this paper constructs an intuitionistic fuzzy neighborhood classifier (IFNEC) by combining NEC with the intuitionistic fuzzy set (IFS) and defines the membership degree and non-membership degree of the object in the neighborhood to depict characteristics of local data. In IFNEC, the multi-attribute decision matrix is used in the decision-making process, which is constructed by a support function and intuitionistic fuzzy aggregation operator to filter the information with large uncertainty. Finally, taking seven data sets from UCI, and using accuracy and F1-score as evaluation indicators, we conduct a comparative experiment between NEC and IFNEC. The experimental results show that IFNEC has better performance than NEC. [ABSTRACT FROM AUTHOR]

To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making. [ABSTRACT FROM AUTHOR]

Grey target decision-making, as an effective method for multi-attribute decision problems, has been applied to evaluations in various domains. However, existing grey target decision-making method fails to mitigate the inherent subjectivity of decision-makers' preferences and cannot address the dependency issues in raw data. To address these limitations, this paper proposes an extended model of grey target decision-making based on prospect theory in a dual hesitant fuzzy environment. Firstly, by referencing the positive, negative, and median expected points of each dual hesitant fuzzy decision matrix and employing the prospect theory value function for numerical transformation, a dual hesitant fuzzy prospect matrix is formed. Secondly, utilizing the projection distance and the rewardpenalty principle, the comprehensive target center distance of the decision matrix is calculated to identify the superiority or inferiority of different alternatives. Furthermore, a nonlinear model with minimal comprehensive target center distance is established based on the principle of maximum entropy to optimize attribute weights. Finally, the effectiveness and rationality of the proposed decision-making method are validated through a case study of ecological assessment in the aviation industry cluster. [ABSTRACT FROM AUTHOR]

A continuous attribute (e.g., calorie count) can be classified into separate categories (e.g., high vs. low), and a similar attribute value can fall into different categories depending on where the category boundaries are drawn. This research explores the effect of categorization on judgments of options (e.g., products and incentive‐compatible games) with continuous attributes. I predict and find a systematic preference shift between two options that were presented with different categorization criteria: When two options involve a tradeoff between two continuous attributes, people tend to prefer the option with both attributes classified into the favorable categories given the categorization criteria. I further show that this effect is driven by larger perceived differences between attribute values across category boundaries and is moderated by people's tendency to rely on category information. Overall, this effect holds even when people are highly familiar with the attributes and feel confident to make similarity evaluations, when people are cued that the categories provide little informational value, and when people are incentivized to make deliberate decisions. The findings in this research carry both theoretical and practical implications. [ABSTRACT FROM AUTHOR]

In multi-attribute decision making (MADM), complex situations often arise where decision attributes are interval-valued hesitant fuzzy numbers (IVHFNs) and the attributes are interrelated. Traditional decision-making methods may be ineffective in handling such cases, highlighting the practical importance of seeking more effective approaches. Therefore, finding a more effective decision-making approach has important practical significance. By combining the theories of Archimedean S-norms and T-norms, we innovatively propose a multi-attribute decision-making method based on the generalized interval-valued hesitant fuzzy weighted Heronian mean (GIVHFWHM) operator to address the aforementioned issues. Initially, based on the operational laws of IVHFNs and the Heronian mean (HM) operator, we introduce the generalized interval-valued hesitant fuzzy Heronian mean (GIVHFHM) operator and the GIVHFWHM operator. We then examine properties of the GIVHFHM operator, including permutation invariance, idempotency, monotonicity, boundedness, and parameter symmetry. A multi-attribute decision-making model is constructed based on the GIVHFWHM operator. Finally, we validate the proposed model through numerical experiments in MADM. The results demonstrate that the new decision-making method, based on the GIVHFWHM operator, is feasible and effective in handling multi-attribute decision problems involving IVHFNs with interdependent attributes. This approach provides a novel perspective and method for solving MADM problems under interval-valued hesitant fuzzy conditions with interdependent attributes. It enriches the theoretical framework of multi-attribute hesitant decision models and expands the application of the Heronian mean operator within interval-valued hesitant fuzzy environments. This methodology assists decision makers in making more accurate decisions within complex decision-making contexts, enhancing both the scientific rigor and reliability of decision-making processes.

In the traditional decision-making process for product form design, designers and experts often prioritize schemes based on their own knowledge and experience. This approach can lead to an oversight of user preferences, ultimately affecting decision outcomes. In contrast, crowd-intelligence-driven, multi-attribute decision-making for product form design in the cloud environment builds upon traditional approaches by leveraging the vast and diverse expertise of individuals on cloud platforms, engaging participants from various fields and roles in the decision-making process to enhance comprehensiveness and accuracy. To address the issue of a single decision-maker and limited user participation in the decision-making process for product form design schemes in the cloud environment, a multi-attribute decision-making method integrating expert knowledge and user preferences is proposed. This method aims to select a product form design scheme that optimally balances expert and user satisfaction. Initially, the Pythagorean Hesitant Fuzzy Set (PHFS) is used to quantify qualitative product attributes and to establish a comprehensive multi-attribute evaluation system. In the aspect of expert decision-making, a gray correlation coefficient decision matrix based on expert knowledge is established and the overall score of the base alternative is calculated by the ViseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method and the Improved Osculating Value method. In terms of user decision-making, weights are determined by calculating the similarity between user evaluation matrices, and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to calculate scores for product form designs based on user preferences. Ultimately, optimal selection is achieved by aggregating the aforementioned expert evaluation values and user preference values. The method’s effectiveness and feasibility are confirmed through a case study of coffee machine product form design schemes.

Emergency rescue decisions in case of a typhoon disaster can be considered multi-attribute decision-making problems. Considering the need for the timeliness and authenticity of decision-making information sources after such a disaster, this study proposed using learning methods to process real-time online data and interval-valued neutrosophic numbers (NNs) to express the classification results. Using Typhoon Hagupit as an example, a trained text classification model was used to classify real-time data (online comments), following which the classification results were used as weights to convert these data into interval-valued NNs. Finally, the technique for order of preference by similarity to ideal solution (TOPSIS) method was adopted to rank the extent of damage caused by the typhoon in each region; the sorting results were consistent with the official statistical data, proving the effectiveness of the proposed method. A detailed sensitivity analysis was conducted to determine the optimal parameter settings of the classification model. Furthermore, the proposed method was compared with existing methods in terms of data conversion and deep learning efficiency; the results confirmed the superior capabilities of the proposed method. Notably, the proposed method can provide support to disaster management professionals in their post-disaster emergency relief work. [ABSTRACT FROM AUTHOR]

Z-numbers contain fuzzy restrictions, credibility measures, and probability distributions to effectively represent uncertain information. Converting Z-numbers to fuzzy numbers facilitates extensive applications (such as multi-attribute decision-making (MADM)), thus becoming valuable for research purposes. Regarding Z-number conversions, the original method never considers the association probability, while probabilistic strategies offer better informatization. Recently, a probability-driven conversion starts with a linear transformation of the centroid difference between the fuzzy restriction and probabilistic distribution. However, it has the invalidation weakness of edge information due to underlying non-normalization. To improve this probability-linear conversion, a Z-number conversion is proposed by using underlying probability-exponential descriptions, and this new method is further applied to MADM. At first, the current probability-linear conversion is analyzed based on the initial non-probabilistic conversion, and its intrinsic weakness and correctional improvement are revealed. Then, the novel probability-exponential conversion resorts to an exponential characterization of centroid difference between the restriction and distribution, and it gains information enrichment due to underlying normalization. The refined method preserves the inherent characteristics of Z-numbers more effectively, facilitating their application in subsequent engineering practices. This is especially pertinent in decision-making systems based on expert input and initial value problems. The proposed method for converting Z-numbers aims to minimize information loss in transitions between Z-numbers and classical fuzzy numbers. This approach will be further explored in future research. Furthermore, the probability-exponential conversion induces an ExpTODIM algorithm for MADM, called PE-ExpTODIM. Three Z-number conversions (i.e., the non-probabilistic, probability-linear, and probability-exponential types) and three decision algorithms (i.e., ExpTODIM, EDAS, MOORA) are combined to establish a 3 × 3 framework of Z-number-driven MADM. Finally, the systematical 9 algorithms are applied to the problem of site selection of carbon storage. They are validated by criss-cross contrast analyses and statistical significance tests. Thus, PE-ExpTODIM exhibits the desired optimization. The last technology of statistical testing is original, ingenious, and valuable for MADM. [ABSTRACT FROM AUTHOR]

The T-spherical fuzzy set (T-SFS) has been widely used in multi-attribute decision-making (MADM) problems due to its powerful expression ability for uncertain information. The evidential reasoning (ER) method can avoid the information loss when aggregating the evaluation values of an alternative with regard to all attributes, which can prevent the decision result from being dominated by extreme evaluation values. Considering the significant advantage of the ER method in information aggregation, this paper develops a new aggregation model assimilating the T-SFSs and the ER method, which is called evidential T-spherical fuzzy MADM (ET-SFMADM). The ET-SFMADM can prevent information loss in the decision process, so as to obtain a correct ranking of the alternatives. Furthermore, this paper also proposes a T-spherical fuzzy cross entropy (T-SFCE) to determine the weights of attributes, which can reduce dependence on decision-makers. Finally, the viability of the ET-SFMADM is illustrated through a numerical example for the implementation effect of the hierarchical medical treatment system in different regions, and further the sensitivity analysis and comparison analysis with existing MADM methods are carried out to demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

The hotel industry in Iran faces critical challenges that underscore the urgent need for sustainable practices, specifically in the realms of energy, water, and food. Despite industry growth, a mere three percent of hotels fall into the five- and four-star categories, emphasizing the need for widespread adoption of sustainable practices. Focused on Ramsar in Mazandaran, the study underscores the importance of eco-friendly strategies to tackle challenges related to the food–water–energy nexus. Employing the SCOC, Fuzzy BWM, and Z-MARCOS methods, the research proposes a robust framework for evaluating hotel development strategies. The case study reveals a concentration of hotels in Khorasan Razavi, Mazandaran, and Tehran, urging prioritization of sustainable practices in these regions. Analyzing Ramsar's climate, the study suggests leveraging solar energy and implementing green roofs, emphasizing an integrated approach to achieve eco-friendly hotel construction. Furthermore, the research provides a prioritized set of strategies based on SCOC, aligning with criteria regarding the water–energy–food nexus. It emphasizes internal strengths, opportunities, and strategic technology partnerships while acknowledging external challenges such as political stability and climate change risks. The discussion introduces an Importance–Performance Analysis (IPA) to guide managerial decisions, presenting an insightful perspective for effective strategy implementation in Iran's evolving hotel industry. [ABSTRACT FROM AUTHOR]

When handling complex uncertainty information for multi-attribute decision-making (MADM) problems, interval-valued Fermatean fuzzy sets (IVFFSs) are a novel and powerful tool with a wide range of prospective applications. However, existing MADM methods based on IVFFS ignore associations between attributes and are vulnerable to extreme values. Thus, this research proposes a novel MADM method based on IVFFSs. First, taking into consideration attribute relationships, we propose interval-valued Fermatean fuzzy Bonferroni mean (IVFFBM) operators and interval-valued Fermatean fuzzy weighted Bonferroni mean (IVFFWBM) operators based on IVFFSs. Further, interval-valued Fermatean fuzzy power Bonferroni mean (IVFFPBM) operator and interval-valued Fermatean fuzzy weighted power Bonferroni mean (IVFFWPBM) operator are suggested considering the impact of extreme values. Secondly, Attribute weights are a key component of MADM. A novel method for determining attribute weights based on fuzzy entropy is developed. Finally, a novel MADM approach is proposed based on the proposed operator and weight determination method. Experimental results on one real-life case demonstrate the superiority and effectiveness of our method. [ABSTRACT FROM AUTHOR]

The goal of this study is to bring neutrosophic structured element theory into the assessment of the entrepreneurial orientation of online peer-to-peer lending platforms, as well as to simplify the complicated processes of conventional neutrosophic decision making. This study discusses several methods for assessing the entrepreneurial orientation of online P2P lending systems. Two strategies are offered to deal with the triangular single-valued neutrosophic number multiple attribute decision making issues with incomplete definite knowledge on criteria's weights using the neutrosophic structured element approach. In terms of computational efficiency and performance, the recommended techniques produced encouraging results. The proposed methodologies are easy in understanding and computation, have a great lot of practical utility, and provide new concepts for applying neutrosophic structured element theory to neutrosophic MADM issues and other fields. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term sets (PLTSs) may convey flexible and accurate qualitative information to decision-makers, and it has been widely utilized to handle multi-attribute decision-making (MADM) issues. This article presents a novel technique for MADM using probabilistic linguistic information where attribute weights are entirely unknown and interactive. Firstly, we define the covariance matrix for the set of PLTSs and investigate its properties. Secondly, we propose the probabilistic linguistic Mahalanobis–Taguchi System (PL-MTS) by extending the Mahalanobis–Taguchi System (MTS) to the probabilistic linguistic environment. Using PL-MTS, fuzzy measures of attributes are then computed. Thirdly, this article modifies the current probabilistic linguistic Choquet integral (PLCI) operator and proposes the probabilistic linguistic geometric Choquet integral (PLGCI) operator and the probabilistic linguistic average Choquet integral (PLACI) operator. Fourthly, the decision information of all alternatives is aggregated using PLGCI and PLACI operators, and the alternatives are ordered according to the comparison rules of PLTSs. Finally, an illustration of supplier selection is provided to validate the efficacy of the method. [ABSTRACT FROM AUTHOR]

The present investigation has centered on examining the imp act of vegetation-based management strategies on the socio-economic, physical, and ecological aspects of the Aghsu watershed in Golestan province, with a particular emphasis on mitigating soil erosion and flooding issues. This study implemented four biological interventions (namely contour furrows with seedling planting, reforestation, channel terraces with tree planting, and agroforestry) and identified 16 management scenarios based on the managerial issues of the area. To establish a hierarchy of management scenarios, the techniques of TOPSIS, SAW, linear assignment, and VIKOR were employed, in conjunction with four distinct weighting methodologies (namely, Shannon Entropy, AHP, ANP, and adjusted weight). The Borda method has been employed to amalgamate the ranking of the suggested technique. Based on the results obtained from all proposed methods for prioritizing scenarios, it has been confirmed that "Scenario 1" holds the lowest priority. The findings indicate that "Scenario 3" (Agroforestry) and "Scenario 6" (Agroforestry and Contour furrows with planting of seedling) represent the optimal scenario groups. The findings indicate that the amalgamation of two scenarios and scenarios that incorporate Agroforestry exhibit superior outcomes. The implementation of agroforestry is a noteworthy endeavor that warrants heightened attention, with other management pursuits being regarded as secondary priorities. Moreover, it can be asserted that the precise weighting of evaluation criteria plays a crucial role in prioritizing management scenarios. The precise computation of weights is imperative. The utilization of a scenario-based methodology in this study facilitates the prediction of the potential outcomes of biologic management interventions. The utilization of this methodology is postulated to enable watershed planners and stakeholders to select the optimal scenario from the proposed set of management scenarios. [ABSTRACT FROM AUTHOR]

Sustainable supplier selection (SSS) is an essential part of the decision-making process in sustainable supply chains. Numerous research studies have been conducted using various decision-making methods to attend to this research-worthy issue. This literature review presents a comprehensive SSS analysis focusing on social, economic, and environmental aspects. The present study spans five years (2018–2022) and considers 101 papers. It provides a detailed breakdown of the papers based on their dates of publication, the countries of the writers, application fields, and journals, and it categorizes them based on their approaches. In addition, this review examines the use of single- or hybrid-form methodologies in the papers reviewed. It also identifies that the TOPSIS, AHP, VIKOR, BWM, DEA, DEMATEL, and MULTIMOORA methods and their extensions are the most frequently used methods in SSS studies. It is concluded that hybrid approaches and their rough, grey, and fuzzy extensions are used to solve real-world problems. However, state-of-the-art mathematical tools, such as soft sets and their hybrid versions with fuzzy sets, have not been utilized in SSS studies. Therefore, this study inspires and encourages the use of such tools in SSS research. [ABSTRACT FROM AUTHOR]

Cubic Fermatean fuzzy sets offer a flexible and powerful tool for decision-making, permitting decision-makers to incorporate uncertainty and reluctance into their decision-making process, and enabling them to make more informed and effective decisions in complex and uncertain situations. We present cubic fermatean fuzzy set and operational laws. We offer some cubic fermatean fuzzy numbers, as well as some cubic fermatean fuzzy aggregation operators, such as the cubic fermatean Einstein fuzzy weighted geometric operator, the cubic fermatean Einstein fuzzy ordered weighted geometric operator, and the cubic fermatean Einstein fuzzy hybrid weighted geometric operator. To demonstrate the solution to complicated real-life problems, an algorithm for the MADM problem is established under a system of cubic fermatean fuzzy information. To check the possibility of proposed aggregation approaches, we provided a numerical example to choose the desirable best options by using conceived approaches. To disclose the suppleness and applicability of designed methods, sensitive study, and comparative study are illustrated by complementary findings of existing methods with presently developed approaches.

The consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with enhanced capabilities in depicting ambiguous information. The Bonferroni operator proficiently mitigates the influences of interrelations between attributes in decision-making dilemmas. To address the Multi-Attribute Decision Making (MADM) conundrum wherein attribute values are associative Triangular Pythagorean Fuzzy Numbers (TPFNs), a novel methodology leveraging the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Mean (GTPFWBM) operator and the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Geometric Mean (GTPFWBGM) operator is advanced. Initiating with the foundational Triangular Pythagorean Fuzzy Set and the Generalized Bonferroni Mean (GBM) operator, both the GTPFWBM and GTPFWBGM operators are delineated. Subsequent exploration dives into the intrinsic properties of these pioneering operators, encompassing facets like reducibility, permutation invariance, idempotency, monotonicity and boundedness. Building upon this foundation, a MADM methodology predicated on the GTPFWBM and GTPFWBGM operators is conceptualized. The culmination of this research underscores the method's rationality and practicality, illustrated through a venture capital investment exemplar.

In recent years, waste management approaches have shifted to recycling and recovery, and waste is now viewed as a potentially new resource. Several research projects have developed extensive plans to observe the planning in these waste management systems. These plastic recycling methods contribute to the creation of environmentally friendly products from waste. In this study, we present a method of multi-attribute decision making (MADM) to provide an efficient way to choose the best plastic recycling method from the selected four recycling alternatives. The multi-attribute border approximation area comparison (MABAC) method is used to evaluate the alternatives under the single-valued neutrosophic fuzzy set (SVNFS). Additionally, we used SWARA in computing the weights of the attributes. Finally, a numerical illustration is given for this problem.

At present, the performance demand of power communication service for bearer network is constantly increasing. Software Defined Optical Network (SDON) technology drives the integration of power communication and SDON technology with its advantages of openness and softwareization. The index system and evaluation method established based on traditional optical transmission network cannot reflect the characteristics of SDON architecture and its influence on bearer performance of power communication network service. In this paper, a new index system is constructed based on the performance requirements, influencing factors and the influence of different SDON architectures on the service performance of power communication business. The decision matrix was determined according to the contribution degree of the index to each attribute. The Ordered Weighted Average-Extended-Technique for Order of Preference by Similarity to Ideal Solution (OWA-E-TOPSIS) multi-attribute decision making method was proposed to realize the index screening. The weight distribution of the selected indicators is carried out by Analytic Hierarchy Process (AHP), and the examples are collected. After the pretreatment by utility function method, the index value aggregation is carried out. By comparing the evaluation results of each instance, the feasibility of the index system and evaluation method are verified, which provided a basis for the application of new technology and new business support of electric power communication network.