Configurational paths to turnover intention among primary public health workers in Liaoning Province, China: a fuzzy-set qualitative comparative analysis.

BACKGROUND: A stable public health workforce plays an indispensable role in the realization of the goal of health for all. However, there is an exodus of public health workers from the Centers for Disease Control and Prevention (CDC). Given the limited evidence on the mechanisms shaping turnover intention (TI) among public health workers, the study aims to investigate the triggering mechanisms of high and low turnover intention by combining job demands, job resources, and personal resources through a set theory perspective based on the Job-Demand-Resources (JD-R) model. METHODS: The cross-sectional study was conducted from September 7 to 18, 2020 at district (county) level CDC in Liaoning Province, China. A total of 584 public health professionals were included. Overcommitment, effort, social respect, occupational identity, job rewards, self-efficacy, and psychological resilience were included in the study as configuration factors. The data were gathered through an online questionnaire and were analyzed using multiple regression and fuzzy-set Qualitative Comparative Analysis (fsQCA). RESULTS: Social respect (B = -0.682, P < 0.001), occupational identity (B = -0.168, P < 0.001), and effort (B = 0.114, P < 0.001) were associated with turnover intention. Five configurations for high turnover intention and five for low turnover intention were obtained through the fsQCA, with occupational identity and effort playing an essential role in all pathways. Moreover, the configurations for low turnover intention are not the antithesis of the configurations for high turnover intention. CONCLUSION: Managers should synthesize the combined effects of factors when implementing interventions and formulating policies. Given the vital role of occupational identity and effort, mechanisms for the rational distribution of work to avoid excessive efforts and measures to promote occupational identity should be implemented to reduce the turnover intentions of primary public health workers and encourage their intention to stay.

Evaluation of food waste treatment techniques using the complex q-rung orthopair fuzzy generalized TODIM method with weighted power geometric operator.

Food waste has received wide attention due to its hazardous environmental effects, such as soil, water, and air pollution. Evaluating food waste treatment techniques is imperative to realize environmental sustainability. This study proposes an integrated framework, the complex q-rung orthopair fuzzy-generalized TODIM (an acronym in Portuguese for interactive and multi-criteria decision-making) method with weighted power geometric operator, to assess the appropriate technique for food waste. The assessment of food waste treatment techniques can be divided into three phases: information processing, information fusion, and ranking alternatives. Firstly, the complex q-rung orthopair fuzzy set flexibly describes the information with periodic characteristics in the processing process with various parameters q. Then, the weighted power geometric operator is employed to calculate the weight of the expert and form the group evaluation matrix, in which the weight of each input rating depends upon the other input ratings. It can simulate the mutual support, multiplicative preferences, and interrelationship of experts. Next, the generalized TODIM method is employed to rank the food waste treatment techniques, considering experts' psychological characteristics and bounded behavior. Subsequently, a real-world application case examines the practicability of the proposed framework. Furthermore, the sensitivity analysis verifies the validity and stability of the presented framework. The comparative study highlights the effectiveness of this framework using the existing frameworks. According to the result, Anaerobic digestion (0.0043) has the highest priority among the considered alternatives, while Incineration (-0.0009) has the lowest.

Probabilistic Hesitant Fuzzy Evidence Theory and Its Application in Capability Evaluation of a Satellite Communication System.

Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities.

Factors influencing the complex problem-solving skills in reflective learning: results from partial least square structural equation modeling and fuzzy set qualitative comparative analysis.

BACKGROUND: The Organization for Economic Cooperation and Development emphasizes the importance of complex problem-solving (CPS) skills in the 21st century. CPS skills have been linked to academic performance, career development, and job competency training. Reflective learning, which includes journal writing, peer reflection, selfreflection, and group discussion, has been explored to improve critical thinking and problem-solving abilities. The development of various thinking modes and abilities, such as algorithmic thinking, creativity, and empathic concern, all affect problem-solving skills. However, there is a lack of an overall theory to relate variables to each other, which means that different theories need to be integrated to focus on how CPS skills can be effectively trained and improved. METHODS: Data from 136 medical students were analyzed using partial least square structural equation modeling (PLSSEM) and fuzzy set qualitative comparative analysis (fsQCA). A hypothesized model examining the associations between the CPS skills and influence factors was constructed. RESULTS: The evaluation of the structural model showed that some variables had significant influences on CPS skills, while others did not. After deleting the insignificant pathways, a structural model was built, which showed that mediating effects of empathic concern and critical thinking were observed, while personal distress only had a direct effect on CPS skills. The results of necessity showed that only cooperativity and creativity are necessary conditions for critical thinking. The fsQCA analysis provided clues for each different pathway to the result, with all consistency values being higher than 0.8, and most coverage values being between 0.240 and 0.839. The fsQCA confirmed the validity of the model and provided configurations that enhanced the CPS skills. CONCLUSIONS: This study provides evidence that reflective learning based on multi-dimensional empathy theory and 21 stcentury skills theory can improve CPS skills in medical students. These results have practical implications for learning and suggest that educators should consider incorporating reflective learning strategies that focus on empathy and 21 stcentury skills to enhance CPS skills in their curricula.

A novel MCDM approach to selecting a biodegradable dynamic plastic product: a probabilistic hesitant fuzzy set-based COPRAS method.

The development of biodegradable polymers for both industrial and commercial uses is crucial nowadays due to the detrimental environmental effects of synthetic plastics. For a variety of uses, researchers have created numerous starch-based composites. The current study examines bioplastics made from maize and rice starch for packaging purposes. Several types of bioplastic samples are created using various ratios of gelatin, glycerol, citric acid, maize starch, and rice starch. People have discovered the value of plastics all around the world. It can be used for packaging, trash bags, liquid containers, throwaway quick service restaurant products, and other things. Regarding the negative aspect of plastics, their dumping after durability poses a serious risk to both people and wildlife. This prompted researchers to seek alternative natural resources that may be used to create flexible polymers that are recyclable, eco-friendly, and sustainable. It has been discovered that tuber and grain starches can be used to produce flexible biopolymers. The decision to choose the best among these choices is an MCDM problem because the carbohydrates from these suppliers have varying qualities. The Probabilistic Hesitant Fuzzy Set (PHFS)-based COmplex PRoportional ASsessment (COPRAS) method for solving uncertainty problems is utilized in this research study. To get the objective weights of the criteria in this case, we used the Critic method of weight determination. An example case of selecting the optimal hydrolyzes for biodegradable dynamic plastic synthesis was chosen to represent the applicability of the suggested approach. The findings demonstrate the feasibility of thermoplastic starches derived from rice and corn for packaging applications.

What contributes to local-level institutional adaptation under climate change? A configurational approach based on evidence from China's Sponge City Program.

Unrestrained human industrial and agricultural production activities exacerbate climate change and environmental pollution. Climate change leads to an increase in flood risks and the spread of water and soil pollution, resulting in challenges in urban stormwater management. Institutional adaptation to climate change is vital for realizing effective local urban stormwater management. However, the accumulated knowledge on climate adaptation over the past decade has been concentrated at the technical and economic levels, with limited research on institutional adaptation. The Sponge City Program in China selects 30 pilot cities to promote a novel stormwater management approach that combines the reliability of traditional gray infrastructures made of concrete materials with the adaptability and sustainability of green-blue infrastructures based on natural-based solutions, but the extent of institutional adaptation in this process varies considerably across pilot cities. To explain what drives institutional adaptation, a configurational analysis of pilot cities is conducted using the fuzzy-set qualitative comparative analysis method. Based on data from 628 official reports and 36 interviews, we demonstrate local governments are significant institutional entrepreneurs, and high institutional adaptation occurs with the combined effects of institutional capacity, financial resources, and reputational incentives. There are three types of paths driving institutional adaptation: "strong institutional capacity-strong financial resource-low reputational reserve," "strong institutional capacity-strong financial resource-high reputational competition," and "strong institutional capacity-weak financial resource-low reputational reserve." These three paths account for 72% of the instances of high institutional adaptation outcomes, and 90% of cases share a given configuration of conditions associated with an outcome. Our conclusion advances a theoretical understanding of the drivers of institutional adaptation and provides guidelines for future climate adaptation practices.

New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach.

The most straightforward approaches to checking the degrees of similarity and differentiation between two sets are to use distance and cosine similarity metrics. The cosine of the angle between two n-dimensional vectors in n-dimensional space is called cosine similarity. Even though the two sides are dissimilar in size, cosine similarity may readily find commonalities since it deals with the angle in between. Cosine similarity is widely used because it is simple, ideal for usage with sparse data, and deals with the angle between two vectors rather than their magnitude. The distance function is an elegant and canonical quantitative tool to measure the similarity or difference between two sets. This work presents new metrics of distance and cosine similarity amongst Fermatean fuzzy sets. Initially, the definitions of the new measures based on Fermatean fuzzy sets were presented, and their properties were explored. Considering that the cosine measure does not satisfy the axiom of similarity measure, then we propose a method to construct other similarity measures between Fermatean fuzzy sets based on the proposed cosine similarity and Euclidean distance measures and it satisfies the axiom of the similarity measure. Furthermore, we obtain a cosine distance measure between Fermatean fuzzy sets by using the relationship between the similarity and distance measures, then we extend the technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.

Sustainability and capability-based assessment of marine oil spill response technologies using a decision support system under decomposed fuzzy set.

Marine oil spills are a practically challenging environmental occurrence to remediate. The critical stage of managing marine oil spills is choosing an appropriate response technology. This research implements a novel sustainability and capability policy-oriented decision support system (DSS) and the decomposed fuzzy set-based ORESTE model. First, an integrated criteria system on the basis of the sustainability and capability aspects is employed by considering four social, environmental, economic, and capability dimensions. Second, the ORESTE model under the decomposed fuzzy environment is extended to deal with the uncertainty data, evaluate the conflicts between the candidate alternatives, and choose the optimal scenario. Seven technologies of bioremediation, solidifiers, dispersants, adsorbents, in situ burning, booms, and skimmers for remediating oil spills in the Persian Gulf, Iran, have been assessed. The assessment results indicate that the bioremediation technology is the optimal scenario for the oil spill-contaminated sites management and the suggested DSS is feasible and applicable.

A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic.

The outbreak of Corona Virus Disease 2019 (COVID-19) makes people more concerned about the validity and timeliness of emergency decision making. When an emergency occurs, it is difficult for decision makers (DMs) to give accurate assessment information in the early stage due to the urgency of time, the incompleteness of information, and the limitations of DMs' cognition and knowledge. Hence, we use interval-valued intuitionistic hesitant fuzzy sets rather than exact numbers to better characterize the fuzziness and uncertainty of emergencies. In addition, the Internet has become a major platform for the public to express their opinions or concerns, so we can collect the user-generated content on social media to help DMs determine appropriate emergency decision-making criteria which are the premise and basis of scientific decisions. However, there is likely to be some correlation between the obtained criteria. To this end, we first extend the Bonferroni mean (BM) operator to the interval-valued intuitionistic hesitant fuzzy environment, and propose three interval-valued intuitionistic hesitant fuzzy BM operators to capture the interrelation of fuzzy input variables, including an interval-valued intuitionistic hesitant fuzzy BM operator, a simplified interval-valued intuitionistic hesitant fuzzy BM operator, and a simplified interval-valued intuitionistic hesitant fuzzy weighted BM (SIVIHFWBM) operator. Then, a new group emergency decision-making method based on the SIVIHFWBM operator and social media data is proposed, and the specific steps of ranking all emergency plans are put forward. Moreover, our method is applied to evaluate emergency plans for the prevention and control of COVID-19. Finally, the effectiveness and feasibility of the method are verified by the sensitivity analysis, validity test, and comparative analysis.

An integrated interval-valued intuitionistic fuzzy technique for resumption risk assessment amid COVID-19 prevention.

Currently, China has achieved a remarkable achievement on the containment of COVID-19, which creates a favorable condition for the gradual resumption of normal life. However, COVID-19 infections continue to rise in many nations and some sporadic cases occur from time to time in China, which still poses some risks to the resumption. Hence, it is imperative to develop some reasonable techniques to assess the resumption risk. This paper aims to investigate an integrated interval-valued intuitionistic fuzzy (IVIF) technique to adroitly assess the resumption risk based on DEMATEL (decision making trial and evaluation laboratory), BWM (best-worst method) and SPA (set pair analysis). This integrated technique is called IVIF-DBWM-SPA, where the IVIF-DBWM (combined by the IVIF-DEMATEL and IVIF-BWM) is used to determine the global criteria weights and the IVIF-SPA is employed to generate the ranking order of the alternatives. The IVIF-DEMATEL and IVIF-BWM are used to determine the weights of dimensions and the weights of criteria under each dimension, respectively. In this IVIF-BWM, two bi-objective programming models are constructed by regarding experts' pessimistic and optimistic attitudes, respectively. Combined experts' intrapersonal and interpersonal uncertainties simultaneously, a bi-objective programming model is proposed to derive the dynamic weights of experts. Based on the determined weights of experts and criteria, an IVIF-SPA is developed to assess the risk levels of all alternatives. The validity of the proposed technique is demonstrated with a real case of college resumption risk assessment amid COVID-19. Some sensitivity and comparison analyses are provided to show the merits of the proposed technique.

Configurational patterns for COVID-19 related social media rumor refutation effectiveness enhancement based on machine learning and fsQCA.

Infodemics are intertwined with the COVID-19 pandemic, affecting people's perception and social order. To curb the spread of COVID-19 related false rumors, fuzzy-set qualitative comparative analysis (fsQCA) is used to find configurational pathways to enhance rumor refutation effectiveness. In this paper, a total of 1,903 COVID-19 related false rumor refutation microblogs on Sina Weibo are collected by a web crawler from January 1, 2022 to April 20, 2022, and 10 main conditions affecting rumor refutation effectiveness index (REI) are identified based on "three rules of epidemics". To reduce data redundancy, five ensemble machine learning models are established and tuned, among which Light Gradient Boosting Machine (LGBM) regression model has the best performance. Then five core conditions are extracted by feature importance ranking of LGBM. Based on fsQCA with the five core conditions, REI enhancement can be achieved through three different pathway elements configurations solutions: "Highly influential microblogger * high followers' stickiness microblogger", "high followers' stickiness microblogger * highly active microblogger * concise information description" and "high followers' stickiness microblogger * the sentiment tendency of the topic * concise information description". Finally, decision-making suggestions for false rumor refutation platforms and new ideas for improving false rumor refutation effectiveness are proposed. The innovation of this paper reflects in exploring the REI enhancement strategy from the perspective of configuration for the first time.

Vaccine selection for COVID-19 by AHP and novel VIKOR hybrid approach with interval type-2 fuzzy sets.

Decisions in the health industry have a significant impact on human lives. With the COVID-19 pandemic, a global war is being waged. Vaccination is a critical component in this fight. The governments are attempting to offer their citizens the best vaccine for the public based on limitations. However, due to the unique characterizations of countries and the people who live in the country, the definition of "the ideal vaccination" is indefinite. Fuzzy set theory has been an ideal tool to cope with problems involving imprecise information such as the meaning of "ideal" in this case. In this study Interval Type-2 Fuzzy Sets (IT2FSs) will be used to describe uncertainty. This IT2FS structure will be the framework of the AHP (Analytic Hierarchy Process), to determine the criteria weights, and the VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje), to generate a set of optimal choices. The main objective of this study is to sustain the necessary effect of uncertainty of fuzzy sets via the Interval Type-2 Fuzzy (IT2F) metric to the VIKOR method and thus propose an extended VIKOR. The presented new approach will be applied to the problem of vaccine selection for COVID-19. Hence, for the first time in the literature, an application with a multilevel hierarchy will be used in IT2FAHP-VIKOR. Also, obtained optimal solution set with this hybrid framework will be compared with fuzzy AHP-VIKOR and the rankings evaluated with the IT2FTOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and sensitivity analysis will be performed.

An integrated rough-fuzzy WINGS-ISM method with an application in ASSCM.

Environmental deterioration, the COVID-19 pandemic and the Russian-Ukrainian conflict had brought chronic and dramatic impacts on agricultural supply chain around the world, resulting in high inflation rates and unavoidable costs. In order to reduce the adverse impacts and achieve sustainability in agricultural supply chain, it's necessary to scientifically explore composite indicators interlinked with agricultural sustainable supply chain management (ASSCM). The current study developed an integrated rough-fuzzy WINGS-ISM method to reveal the hierarchal and causal structure of indicators. It is found that environmental legislation, regulation, licensing, and government subsidies are the main drivers of ASSCM. Specifically, the government can guide the sustainable development of ASSCM by regulating the business environment. The financial support needs to be enlarged to optimize the structure in science and technology of ASSCM. Moreover, corporates and organizations are highly motivated by the increasing awareness of social responsibility and sustainability consciousness to improve the economic performance and achieve the ASSCM goals. A comparative analysis is proposed to illustrate the practicality and reliability of the results obtained from the proposed method, which can be utilized as a reference in ASSCM.

Modelling and Research on Intuitionistic Fuzzy Goal-Based Attack and Defence Game for Infrastructure Networks.

Network attack and defence games are gradually becoming a new approach through which to study the protection of infrastructure networks such as power grids and transportation networks. Uncertainty factors, such as the subjective decision preferences of attackers and defenders, are not considered in existing attack and defence game studies for infrastructure networks. In this paper, we introduce, respectively, the attacker's and defender's expectation value, rejection value, and hesitation degree of the target, as well as construct an intuitionistic fuzzy goal-based attack and defence game model for infrastructure networks that are based on the maximum connectivity slice size, which is a network performance index. The intuitionistic fuzzy two-player, zero-sum game model is converted into a linear programming problem for solving, and the results are analysed to verify the applicability and feasibility of the model proposed in this paper. Furthermore, different situations, such as single-round games and multi-round repeated games, are also considered. The experimental results show that, when attacking the network, the attacker rarely attacks the nodes with higher importance in the network, but instead pays more attention to the nodes that are not prominent in the network neutrality and median; meanwhile, the defender is more inclined to protect the more important nodes in the network to ensure the normal performance of the network.

COVID-19 medical waste transportation risk evaluation integrating type-2 fuzzy total interpretive structural modeling and Bayesian network.

With the amount of medical waste rapidly increasing since the corona virus disease 2019 (COVID-19) pandemic, medical waste treatment risk evaluation has become an important task. The transportation of medical waste is an essential process of medical waste treatment. This paper aims to develop an integrated model to evaluate COVID-19 medical waste transportation risk by integrating an extended type-2 fuzzy total interpretive structural model (TISM) with a Bayesian network (BN). First, an interval type-2 fuzzy based transportation risk rating scale is introduced to help experts express uncertain evaluation information, in which a new double alpha-cut method is developed for the defuzzification of the interval type-2 fuzzy numbers (IT2FNs). Second, TISM is combined with IT2FNs to construct a hierarchical structural model of COVID-19 medical waste transportation risk factors under a high uncertain environment; a new bidirectional extraction method is proposed to describe the hierarchy of risk factors more reasonably and accurately. Third, the BN is integrated with IT2FNs to make a comprehensive medical waste transportation risk evaluation, including identifying the sensitive factors and diagnosing the event's causation. Then, a case study of COVID-19 medical waste transportation is displayed to demonstrate the effectiveness of the proposed model. Further, a comparison of the proposed model with the traditional TISM and BN model is conducted to stress the advantages of the proposed model.

Synthesis of strategies in post-COVID-19 public sector supply chains under an intuitionistic fuzzy environment.

Entities in public sector supply chains (SCs) often operate independently despite having interdependent objectives. Such a fragmented operational design poses several problems magnified by the presence of necessary public health measures fueled by COVID-19. This work contributes to the domain literature by introducing an overarching framework for synthesizing strategies in public sector SCs. The underlying component is the translation of information from the upstream to the downstream entities of the SCs, which is carried out by a Kano-enhanced quality function deployment. The proposed framework introduces intuitionistic fuzzy (IF) decision maps with the aid of the full consistency method to incorporate inherent interrelationships among strategies in the translation agenda. Under an IF environment that better captures judgment uncertainties, an actual case study of a multi-level public sector SC motivated by a government-funded project under the COVID-19 pandemic is demonstrated in this work. Findings of the case suggest that the government prioritizes meeting all project objectives. This requirement is reflected in the downstream SC. The project planning entity focuses on creating an overarching plan of operations, material request entity on complying with government procurement protocols, and maintaining public health and safety in operations for the procurement entity. Results show the effective synthesis of strategies across the SC, ensuring SC integration and collaboration. The case study demonstrates that maintaining public health and safety is a significant component of post-COVID-19 public sector SCs. Several practical insights on the synthesis of public sector SC strategies are also provided in this work.

An integrated fuzzy-grey relational analysis approach to portfolio optimization.

This paper combines two approaches (Fuzzy set theory and Grey Relational Analysis) for modelling an investor's imprecise linguistic expectations and the uncertain returns of assets. We propose a novel maximization-type risk measure capable of incorporating the investor's individual preferences. The investor provides the expectations of what is considered the "ideal" return from the portfolio. We use Credibility theory to capture the investors' subjective and imprecise expectations in a precise mathematical form. We construct a portfolio return sequence using the assets' actual return data and an ideal sequence based on investors' preferences. Subsequently, we calculate the Grey similitude and the closeness incidence degree between the two sequences. The closer the portfolio return is to the ideal return, the better. In this manner, we develop a new risk measure that can quantify an investor's perception of risk. This measure is intuitive and easy to calculate. It does not involve estimating many parameters, something which would increase the estimation risk. We use a genetic algorithm to solve the resulting portfolio optimization model. We illustrate this method with two case studies: (i) a case study of 100 assets of the U.S. stock market's NASDAQ-100 index and (ii) a case study of 50 assets of the Indian stock market's NIFTY-50 index. We comprehensively analyze the model's out-of-sample performance and discuss its implications. The portfolios obtained using the proposed approach exhibit healthy growth outside the in-sample period. We also compare the out-of-sample performance of the proposed model with several approaches in the literature to establish its superiority.

Adoption of AI in response to COVID-19-a configurational perspective.

Although the importance of artificial intelligence (AI) has often been highlighted in strategic agility and decision outcomes, whether it helps firms strengthen their competitiveness and the means firms use to achieve such competitiveness are still under-researched. Our research thus joins the recent discussion on digitalization trends and strategic responses to COVID-19 to better understand how firms strengthen their competitiveness during such challenging times. Namely, this study incorporates the strategic responses to COVID-19 into the technology-organization-environment (TOE) framework by investigating the impacts of different configurations of TOE contexts and strategic responses on a firm's competitive advantage. We used fuzzy-set qualitative comparative analysis to investigate how TOE contexts and strategic responses integrate into configurations and impact a firm's competiveness. By applying a configurational approach with data from 514 exporting firms in China, we find a strong indication of the equifinality of different strategies, indicating that multiple strategic paths can be used to respond to crises. The adoption of AI, while important, is not sufficient to enhance a firm's competitiveness. Our results stress the significance of data quality, organizational resources and capabilities, and digital business model innovation for AI adoption. We also identify successful strategic paths of AI adoption aversion and ambidextrous strategies. The findings have practical implications for firms seeking effective strategies to respond to future crises and sustain their competitive advantages.

How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy.

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy.

Social Infrastructure and the Alleviation of Loneliness in Europe.

In Europe, individualist societies, in which people more highly value independence, have fewer people who are lonely. Yet these societies also have more people who live alone, a strong determinant of loneliness. Evidence suggests that some unrecognized societal-level resources or characteristics can explain this. We uncover multiple pathways toward a lower degree of loneliness among European societies using an ideal method for this purpose, fuzzy-set qualitative comparative analysis. Using data from the 2014 wave of the European Social Survey and other sources, we analyzed loneliness outcomes among 26 European societies. Our findings suggest two necessary conditions for a low degree of loneliness: high internet access and high association participation. Further, three pathways are sufficient for achieving less loneliness at the societal level. Most societies that have less loneliness follow both the welfare support and cultural support pathways. The third path, commercial provision, is mutually exclusive with welfare support because the former requires a weak welfare state. The surest policy for building societies that have lower rates of loneliness includes the expansion of internet accessibility, the fostering of civil society through association participation and volunteering, and a welfare state that protects potentially vulnerable populations while funding opportunities for social interaction. This article further contributes methodologically by demonstrating "configurational robustness testing," a more comprehensive means to implement current best practices for fuzzy-set qualitative comparative analysis robustness testing.