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This study aims to improve the reliability of emergency safety barriers by using the subjective safety analysis based on evidential reasoning theory in order to develop on a framework for optimizing the reliability of emergency safety barriers.

The emergency event tree analysis is combined with an interval type-2 fuzzy-set and analytic hierarchy process (AHP) method. In order to the quantitative data is not available, this study based on interval type2 fuzzy set theory, trapezoidal fuzzy numbers describe the expert's imprecise uncertainty about the fuzzy failure probability of emergency safety barriers related to the liquefied petroleum gas storage prevent. Fuzzy fault tree analysis and fuzzy ordered weighted average aggregation are used to address uncertainties in emergency safety barrier reliability assessment. In addition, a critical analysis and some corrective actions are suggested to identify weak points in emergency safety barriers. Therefore, a framework decisions are proposed to optimize and improve safety barrier reliability. Decision-making in this framework uses evidential reasoning theory to identify corrective actions that can optimize reliability based on subjective safety analysis.

A real case study of a liquefied petroleum gas storage in Algeria is presented to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology provides the possibility to evaluate the values of the fuzzy failure probability of emergency safety barriers. In addition, the fuzzy failure probabilities using the fuzzy type-2 AHP method are the most reliable and accurate. As a result, the improved fault tree analysis can estimate uncertain expert opinion weights, identify and evaluate failure probability values for critical basic event. Therefore, suggestions for corrective measures to reduce the failure probability of the fire-fighting system are provided. The obtained results show that of the ten proposed corrective actions, the corrective action “use of periodic maintenance tests” prioritizes reliability, optimization and improvement of safety procedures.

This study helps to determine the safest and most reliable corrective measures to improve the reliability of safety barriers. In addition, it also helps to protect people inside and outside the company from all kinds of major industrial accidents. Among the limitations of this study is that the cost of corrective actions is not taken into account.

Our contribution is to propose an integrated approach that uses interval type-2 fuzzy sets and AHP method and emergency event tree analysis to handle uncertainty in the failure probability assessment of emergency safety barriers. In addition, the integration of fault tree analysis and fuzzy ordered averaging aggregation helps to improve the reliability of the fire-fighting system and optimize the corrective actions that can improve the safety practices in liquefied petroleum gas storage tanks.

In this study, a novel framework was proposed to assess the trust in e-government (e-Gov) services under an uncertain environment. The proposed framework was applied in Iranian municipality websites of e-Gov services to evaluate the readiness score of trust in e-Gov services.

A unique hybrid research methodology was proposed. In the first phase, a comprehensive set of indices were determined from an extensive literature review and finalized by employing the fuzzy Delphi method. In the second phase, interval-valued intuitionistic fuzzy set (IVIFS) -was utilized to model the problem's uncertainty with analytic called IVIFS- hierarchy process (AHP) to determine the importance of indices and indicators by assigning the weights. In the third phase, the fuzzy evaluation method (FEM) is followed for assessing the readiness score of indices in case studies.

The findings indicated that “Trust in government” is the most significant index affecting citizen's trust in e-Gov services while “Maintenance and support” has the least impact on user's intention to use e–Gov services.

The study contributes by introducing a unique research methodology that integrates three phases, including fuzzy Delphi, IVIFS AHP and fuzzy evaluation method. Moreover, the fuzzy sets theory helps to reach a more accurate result by modeling the inherent ambiguity of indicators and indices. Interval-valued intuitionistic fuzzy models the ambiguity of experts' judgments in an interval.

The study helps policy makers to monitor wider aspects of trust in e-Gov services as well as understanding their importance. The study enables policy makers to apply the framework to any potential case studies to evaluate the readiness score of indices and recognizing strengths and weakness of trust dimensions as well as recommending advice for improving the situation.

The study is one of the few to indicate significant indices of trust in e-Gov services in developing countries. The study shows the importance of indicators and indices by assigning a weight. Additionally, the framework can assess the readiness score of various case studies.

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.

Pharmaceutical supply chains (PSCs) need a well-operating and faultless logistics system to successfully store and distribute their medicines. Hospitals, health institutes, and pharmacies must maintain extra stock to respond requirements of the patients. Nevertheless, there is an inverse correlation between the level of medicine stock and logistics service level. The high stock level held by health institutions indicates that we have not sufficiently excellent logistics systems presently. As such, selecting appropriate logistics service providers (drug distributors) is crucial and strategic for PSCs. However, this is difficult for decision-makers, as highly complex situations and conflicting criteria influence such evaluation processes. So, a robust, applicable, and strong methodological frame is required to solve these decision-making problems.

To achieve this challenging issue, the authors develop and apply an integrated entropy-WASPAS methodology with Fermatean fuzzy sets for the first time in the literature. The evaluation process takes place in two stages, as in traditional multi-criteria problems. In the first stage, the importance levels of the criteria are determined by the FF-entropy method. Afterwards, the FF-WASPAS approach ranks the alternatives.

The feasibility of the proposed model is also supported by a case study where six companies are evaluated comprehensively regarding ten criteria. Herewith, total warehouse capacity, number of refrigerated vehicles, and personnel are the top three criteria that significantly influence the evaluation of pharmaceutical distribution and warehousing companies. Further, a comprehensive sensitivity analysis proves the robustness and effectiveness of the proposed approach.

The proposed multi-attribute decision model quantitatively aids managers in selecting logistics service providers considering imprecisions in the multi-criteria decision-making process.

A new model has been developed to present a sound mathematical model for selecting logistics service providers consisting of Fermatean fuzzy entropy and WASPAS methods. The paper's main contribution is presenting a comprehensive and more robust model for the ex ante evaluation and ranking of providers.

The aim of this study is to (1) construct a standard framework for assessing the capability of bioenergy enterprises' digital green innovation partners; (2) quantify the choice of partners for digital green innovation by bioenergy enterprises; (3) propose based on a dual combination empowerment niche digital green innovation field model.

Fuzzy set theory is combined into field theory to investigate resource complementarity. The successful application of the model to a real case illustrates how the model can be used to address the problem of digital green innovation partner selection. Finally, the standard framework and digital green innovation field model can be applied to the practical partner selection of bioenergy enterprises.

Digital green innovation technology of superposition of complementarity, mutual trust and resources makes the digital green innovation knowledge from partners to biofuels in the enterprise. The index rating system included eight target layers: digital technology innovation level, bioenergy technology innovation level, bioenergy green level, aggregated digital green innovation resource level, bioenergy technology market development ability, co-operation mutual trust and cooperation aggregation degree.

This study helps to (1) construct the evaluation standard framework of digital green innovation capability based on the dual combination empowerment theory; (2) develop a new digital green innovation domain model for bioenergy enterprises to select digital green innovation partners; (3) assist bioenergy enterprises in implementing digital green innovation practices.

This paper aims to classify journal papers in the context of hybrid quality function deployment QFD and multi-criteria decision-making (MCDM) methods published during 2004–2021.

A conceptual classification scheme is presented to analyze the hybrid QFD-MCDM methods. Then some recommendations are given to introduce directions for future research.

The results show that among all related areas, the manufacturing application has the most frequency of published papers regarding hybrid QFD-MCDM methods. Moreover, using uncertainty to establish a hybrid QFD-MCDM the relevant papers have been considered during the time interval 2004–2021.

There are various shortcomings in conventional QFD which limit its efficiency and potential applications. Since 2004, when MCDM methods were frequently adopted in the quality management context, increasing attention has been drawn from both practical and academic perspectives. Recently, the integration of MCDM techniques into the QFD model has played an important role in designing new products and services, supplier selection, green manufacturing systems and sustainability topics. Hence, this survey reviewed hybrid QFD-MCDM methods during 2004–2021.

The decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.

Four main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.

The worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.

In a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.

The proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.

To the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.

The main purpose of this study is to provide a comprehensive review and critical insights of the application of fuzzy methods in modeling, assessing and understanding the various aspects of green and sustainable supply chains (SSCs).

The present study conducts a systematic literature review (SLR) and bibliometric analysis of 252 research articles. This study employs various tools such as VOSviewer version 1.6.10, Publish or Perish, Mendeley and Excel that aid in descriptive analysis, bibliometric analysis and network visualization. These tools have been used for performing citation analysis, top authors' analysis, co-occurrence of keywords, cluster and content analysis.

The authors have divided the literature into seven application areas and discussed detailed insights. This study has observed that research in the social sustainability area, including various issues like health and safety, labor rights, discrimination, etc. is scarce. Integration of the Industry 4.0 technologies like blockchain, big data analytics, Internet of Things (IoT) with the sustainable and green supply chain (GSC) is a promising field for future research.

The authors' contribution primarily lies in providing the integrated framework which shows the changing trends in the use of fuzzy methods in the sustainability area classifying and consolidating green and sustainable supply chain management (SSCM) literature in seven major areas where fuzzy methods are predominantly applied. These areas have been obtained after the analysis of clusters and content analysis of the literature presenting key insights from the past and developing the conceptual framework for future research studies.

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 study aims to propose a facilitating methodology for the application of Fuzzy FMEA (Failure Mode and Effect Analysis), comparing the traditional approach with fuzzy variations, supported by a case application in the aeronautical sector.

Based on experts' opinions in risk analysis within the aeronautical sector, rules governing the relationship between severity, occurrence, detection and risk factor were defined. This served as input for developing a fuzzyfied FMEA tool using the Matlab Fuzzy Logic Toolbox. The tool was applied to the sealing process in a company within the aeronautical sector, using triangular and trapezoidal membership functions, and the results were compared with the traditional FMEA approach.

The results of the comparative application of traditional FMEA and fuzzyfied FMEA using triangular and trapezoidal functions have yielded valuable insights into risk analysis. The findings indicated that fuzzyfied FMEA maintained coherence with the traditional analysis in identifying higher-risk effects, aligning with the prioritization of critical failure modes. Additionally, fuzzyfied FMEA allowed for a more refined prioritization by accounting for variations in each variable through fuzzy rules, thereby improving the accuracy of risk analysis and providing a more realistic representation of potential hazards. The application of the developed fuzzyfied FMEA approach showed promise in enhancing risk assessment in the aeronautical sector by considering uncertainties and offering a more detailed and context-specific analysis compared to conventional FMEA.

This study emphasizes the potential of fuzzyfied FMEA in enhancing risk assessment by accurately identifying critical failure modes and providing a more realistic representation of potential hazards. The application case reveals that the proposed tool can be integrated with expert knowledge to improve decision-making processes and risk mitigation strategies within the aeronautical industry. Due to its straightforward approach, this facilitating methodology could also prove beneficial in other industrial sectors.

This paper presents the development and application of a facilitating methodology for implementing Fuzzy FMEA, comparing it with the traditional approach and incorporating variations using triangular and trapezoidal functions. This proposed methodology uses the Toolbox Fuzzy Logic of Matlab to create a fuzzyfied FMEA tool, enabling a more nuanced and context-specific risk analysis by considering uncertainties.