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Platform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.

This paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.

In this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.

Firstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

This is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.

PyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.

In addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Paper is original and not submitted elsewhere.

The purpose of this article is to present the idea of a T-spherical hesitant fuzzy set associated with probability and to develop an extended multi-attributive border approximation area comparison (MABAC) method under probabilistic T-spherical hesitant fuzzy (Pt-SHF) settings.

The authors define some basic operational laws for Pt-SHF sets (Pt-SHFSs) and a comparison method of two probabilistic T-spherical hesitant fuzzy numbers (Pt-SHFNs) is proposed. Moreover, some Pt-SHF aggregation operators and the multi-attributive border approximation area comparison (MABAC) method are established under Pt-SHF scenario to solve group decision making problems.

The developed Pt-SHF MABAC method for multi-attribute group decision making (MAGDM) can overcome the drawbacks of conventional MABAC method and limitations for decision makers, which they face while providing their assessment concerning any object.

Clearly, this paper is devoted to MABAC method, MAGDM and probabilistic T-spherical hesitant fuzzy set theory.

The approach established can be used in a variety of scenarios, including decision making, engineering, and economics. An explanatory example is illustrated which shows the superiority and effectiveness of our proposed technique.

If a T-spherical fuzzy MAGDM problem under the probabilistic scenario needs to be evaluated, the involvement of probabilities in fuzzy system will be lost because of no information. This work fills a gap in literature by establishing the notion of probabilistic t-spherical hesitant fuzzy set to deal with the ambiguity, uncertainty in decision making problems.

This paper aims to propose two portfolio selection models with hesitant value-at-risk (HVaR) – HVaR fuzzy portfolio selection model (HVaR-FPSM) and HVaR-score fuzzy portfolio selection model (HVaR-S-FPSM) – to help investors solve the problem that how bad a portfolio can be under probabilistic hesitant fuzzy environment.

It is strictly proved that the higher the probability threshold, the higher the HVaR in HVaR-S-FPSM. Numerical examples and a case study are used to illustrate the steps of building the proposed models and the importance of the HVaR and score constraint. In case study, the authors conduct a sensitivity analysis and compare the proposed models with decision-making models and hesitant fuzzy portfolio models.

The score constraint can make sure that the portfolio selected is profitable, but will not cause the HVaR to decrease dramatically. The investment proportions of stocks are mainly affected by their HVaRs, which is consistent with the fact that the stock having good performance is usually desirable in portfolio selection. The HVaR-S-FPSM can find portfolios with higher HVaR than each single stock and has little sacrifice of extreme returns.

This paper fulfills a need to construct portfolio selection models with HVaR under probabilistic hesitant fuzzy environment. As a downside risk, the HVaR is more consistent with investors’ intuitions about risks. Moreover, the score constraint makes sure that undesirable portfolios will not be selected.

In the era of information overload, the density of tourism information and the increasingly sophisticated information needs of consumers have created information confusion for tourists and scenic-area managers. The study aims to help scenic-area managers determine the strengths and weaknesses in the development process of scenic areas and to solve the practical problem of tourists' difficulty in quickly and accurately obtaining the destination image of a scenic area and finding a scenic area that meets their needs.

The study uses a variety of machine learning methods, namely, the latent Dirichlet allocation (LDA) theme extraction model, term frequency-inverse document frequency (TF-IDF) weighting method and sentiment analysis. This work also incorporates probabilistic hesitant fuzzy algorithm (PHFA) in multi-attribute decision-making to form an enhanced tourism destination image mining and analysis model based on visitor expression information. The model is intended to help managers and visitors identify the strengths and weaknesses in the development of scenic areas. Jiuzhaigou is used as an example for empirical analysis.

In the study, a complete model for the mining analysis of tourism destination image was constructed, and 24,222 online reviews on Jiuzhaigou, China were analyzed in text. The results revealed a total of 10 attributes and 100 attribute elements. From the identified attributes, three negative attributes were identified, namely, crowdedness, tourism cost and accommodation environment. The study provides suggestions for tourists to select attractions and offers recommendations and improvement measures for Jiuzhaigou in terms of crowd control and post-disaster reconstruction.

Previous research in this area has used small sample data for qualitative analysis. Thus, the current study fills this gap in the literature by proposing a machine learning method that incorporates PHFA through the combination of the ideas of management and multi-attribute decision theory. In addition, the study considers visitors' emotions and thematic preferences from the perspective of their expressed information, based on which the tourism destination image is analyzed. Optimization strategies are provided to help managers of scenic spots in their decision-making.

The purpose of this paper is to develop a multi-attribute group decision-making (MAGDM) method under the q-rung orthopair trapezoidal fuzzy environment, which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral (q-ROTrFACI) and employ TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) to consider the risk psychology of decision-makers, to determine the optimal ranking of alternatives.

In MAGDM, q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) are efficient to indicate the quantitative vagueness of decision-makers. The q-ROTrFACI operator is defined and some properties are proved. Then, a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function. Based on the above, a Choquet integral-based TODIM (CI-TODIM) method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.

The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria. Then, an approach is proposed to determine the center point of q--ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed. Furthermore, CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context. The illustration example of business models' solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.

The paper develops a novel CI-TODIM method that effectively solves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers, which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

The purpose of this research is to provide a theoretical framework for complex equipment quality risk evaluation. The primary aim of the framework is to enhance the ability to identify risks and improve risk control efficiency during the development phase.

A novel framework for quality risk evaluation in complex equipment is proposed, which integrates probabilistic hesitant fuzzy set-quality function deployment (PHFS-QFD) and grey clustering. PHFS-QFD is applied to identify the quality risk factors, and grey clustering is used to evaluate quality risks in cases of poor quality information during the development stage. The unfolding function of QFD is applied to simplify complex evaluation problems.

The methodology presents an innovative approach to quality risk evaluation for complex equipment development. The case analysis demonstrates that this method can efficiently evaluate the quality risks for aircraft development and systematically trace back the risk factors through hierarchical relationships. In comparison to traditional failure mode and effects analysis methods for quality risk assessment, this approach exhibits superior effectiveness and reliability in managing quality risks for complex equipment development.

This study contributes to the field by introducing a novel theoretical framework that combines PHFS-QFD and grey clustering. The integration of these approaches significantly improves the quality risk evaluation process for complex equipment development, overcoming challenges related to data scarcity and simplifying the assessment of intricate systems.

This study aims to improve the offshore wind farm (OWF) site selection evaluation index system and establishes a decision-making model for OWF site selection. It is expected to provide helpful references for the progress of offshore wind power.

Firstly, this paper establishes an evaluation criteria system for OWF site selection, considering six criteria (wind resource, environment, economic, technical, social and risk) and related subcriteria. Then, the Criteria Importance Though Intercrieria Correlation (CRITIC) method is introduced to figure out the weights of evaluation indexes. In addition, the cumulative prospect theory and technique for order preference by similarity to an ideal solution (CPT-TOPSIS) method are employed to construct the OWF site selection decision-making model. Finally, taking the OWF site selection in China as an example, the effectiveness and robustness of the framework are verified by sensitivity analysis and comparative analysis.

This study establishes the OWF site selection evaluation system and constructs a decision-making model under the spherical fuzzy environment. A case of China is employed to verify the effectiveness and feasibility of the model.

In this paper, a new decision-making model is proposed for the first time, considering the ambiguity and uncertainty of information and the risk attitudes of decision-makers (DMs) in the decision-making process.

This study aims to develop a cause-effect relationship between criteria that contribute to water security using the Intuitionistic Fuzzy-Decision-Making Trial and Evaluation Laboratory (IF-DEMATEL) method. Differently from the typical DEMATEL which utilizes crisp numbers, this modification introduces intuitionistic fuzzy numbers (IFNs) to enhance judgments in a group decision-making environment. In particular, the linguistic variables used in IF-DEMATEL are defined using the concept of three-tuple of IFNs.

Data with the linguistic variable “influence” were collected from a group of experts in water security via personal unstructured interviews. Seven water security criteria are considered in this study. Computational software was employed to execute the computational procedures of the IF-DEMATEL method. It is anticipated that by taking into account the hesitation degree of IFNs will reflect the scenario in real life, which could lead to precise decision-making.

The results show that “Over-Abstraction”, “Saltwater Intrusion” and “Limited Infrastructures” are the cause criteria that contribute to water security. In addition, the relationship map of influence shows that “Water Pollution” and “Rapid Urbanization” are the most vulnerable criteria as these two criteria are most easily affected by other criteria in a unidirectional relation.

It is anticipated that these findings will serve as useful references for water security management and policymakers.

The present study makes a noteworthy contribution to the modification of DEMATEL where three-tuple of intuitionistic fuzzy numbers are considered in the computations. The present study also provides additional evidence with respect to factors that contribute to water security.

The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

A case study concerning the healthcare facilities in public hospital is addressed.

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.