A Synergistic Multi-Attribute Decision-Making Method for Educational Institutions Evaluation Using Similarity Measures of Possibility Pythagorean Fuzzy Hypersoft Sets

Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such uncertainties.This study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and AND-operations.Some results related to these operations are also modified for pPyFHSS.Additionally,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and results.Lastly,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested system.The algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical models.Similarly,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.

Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets,Aggregation Operators and Basic Uncertainty Information Granule

Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.

Healthcare providers’perspectives on factors influencing their critical care decision-making during the COVID-19 pandemic:An international pilot survey

BACKGROUND Understanding a patient's clinical status and setting priorities for their care are two aspects of the constantly changing process of clinical decision-making.One analytical technique that can be helpful in uncertain situations is clinical judgment.Clinicians must deal with contradictory information,lack of time to make decisions,and long-term factors when emergencies occur.AIM To examine the ethical issues healthcare professionals faced during the coronavirus disease 2019(COVID-19)pandemic and the factors affecting clinical decision-making.METHODS This pilot study,which means it was a preliminary investigation to gather information and test the feasibility of a larger investigation was conducted over 6 months and we invited responses from clinicians worldwide who managed patients with COVID-19.The survey focused on topics related to their professional roles and personal relationships.We examined five core areas influencing critical care decision-making:Patients'personal factors,family-related factors,informed consent,communication and media,and hospital administrative policies on clinical decision-making.The collected data were analyzed using the χ^(2) test for categorical variables.RESULTS A total of 102 clinicians from 23 specialties and 17 countries responded to the survey.Age was a significant factor in treatment planning(n=88)and ventilator access(n=78).Sex had no bearing on how decisions were made.Most doctors reported maintaining patient confidentiality regarding privacy and informed consent.Approximately 50%of clinicians reported a moderate influence of clinical work,with many citing it as one of the most important factors affecting their health and relationships.Clinicians from developing countries had a significantly higher score for considering a patient's financial status when creating a treatment plan than their counterparts from developed countries.Regarding personal experiences,some respondents noted that treatment plans and preferences changed from wave to wave,and that there was a rapid turnover of studies and evidence.Hospital and government policies also played a role in critical decision-making.Rather than assessing the appropriateness of treatment,some doctors observed that hospital policies regarding medications were driven by patient demand.CONCLUSION Factors other than medical considerations frequently affect management choices.The disparity in treatment choices,became more apparent during the pandemic.We highlight the difficulties and contradictions between moral standards and the realities physicians encountered during this medical emergency.False information,large patient populations,and limited resources caused problems for clinicians.These factors impacted decision-making,which,in turn,affected patient care and healthcare staff well-being.

Ubiquitin-specific protease 1 facilitates tumor immune escape from natural killer cells and predicts the prognosis in small cell lung cancer

Objective:Small cell lung cancer(SCLC)is commonly recognized as the most fatal lung cancer type.Despite substantial advances in immune checkpoint blockade therapies for treating solid cancers,their benefits are limited to a minority of patients with SCLC.In the present study,novel indicators for predicting the outcomes and molecular targets for SCLC treatment were elucidated.Methods:We conducted bioinformatics analysis to identify the key genes associated with tumor-infiltrating lymphocytes in SCLC.The functional role of the key gene identified in SCLC was determined both in vitro and in vivo.Results:A significant correlation was observed between patient survival and CD56dim natural killer(NK)cell proportion.Furthermore,we noted that the hub gene ubiquitin-specific protease 1(USP1)is closely correlated with both CD56dim NK cells and overall survival in SCLC.Bioinformatics analysis revealed that USP1 is upregulated in SCLC.In addition,gene set enrichment analysis revealed that USP1 overexpression hinders NK cell-mediated immune responses.By co-cultivating NK-92 cells with SCLC cells,we demonstrated that NK cell cytotoxicity against SCLC could be improved either via USP1 knock-down or pharmacological inhibition.Furthermore,using a nude-mice xenograft tumor model,we noted that USP1 inhibition effectively suppressed tumor proliferation and increased the expression of NK cell-associated markers.Conclusions:Our study findings highlight the importance of NK cells in regulating SCLC.USP1 overexpression can inhibit NK cell-mediated immunity;therefore,USP1 may serve not only as a prognostic biomarker but also as a potential molecular target of SCLC therapy.

Voices that matter:The impact of patient-reported outcome measures on clinical decision-making

The critical role of patient-reported outcome measures(PROMs)in enhancing clinical decision-making and promoting patient-centered care has gained a profound significance in scientific research.PROMs encapsulate a patient's health status directly from their perspective,encompassing various domains such as symptom severity,functional status,and overall quality of life.By integrating PROMs into routine clinical practice and research,healthcare providers can achieve a more nuanced understanding of patient experiences and tailor treatments accordingly.The deployment of PROMs supports dynamic patient-provider interactions,fostering better patient engagement and adherence to tre-atment plans.Moreover,PROMs are pivotal in clinical settings for monitoring disease progression and treatment efficacy,particularly in chronic and mental health conditions.However,challenges in implementing PROMs include data collection and management,integration into existing health systems,and acceptance by patients and providers.Overcoming these barriers necessitates technological advancements,policy development,and continuous education to enhance the acceptability and effectiveness of PROMs.The paper concludes with recommendations for future research and policy-making aimed at optimizing the use and impact of PROMs across healthcare settings.

早期肺康复联合ESCAPE集束化护理对ICU有创机械通气患者呼吸机相关膈肌功能障碍的影响

目的:探讨早期肺康复联合ESCAPE集束化护理对ICU有创机械通气患者呼吸机相关膈肌功能障碍(VIDD)的影响。方法:将2023年2月1日~12月31日综合ICU收治的41例成人有创机械通气患者随机分为实验组20例和对照组21例,其中实验组3例、对照组4例因转出ICU而脱落,最终纳入实验组和对照组各17例。实验组给予早期肺康复训练联合ESCAPE集束化护理,对照组给予ESCAPE集束化护理。比较两组膈肌移动度及增厚率、临床肺部感染评分(CPIS)、急性生理学与慢性健康状况评分(APACHEⅡ)。结果:实验组治疗后膈肌移动度高于治疗前(P<0.05),膈肌增厚率比较差异无统计学意义(P>0.05);实验组治疗后CPIS、APACHEⅡ评分均低于治疗前(P<0.05)。结论:早期肺康复联合ESCAPE集束化护理可改善ICU有创机械通气患者的膈肌移动度,降低肺部感染发生风险、改善健康状况,减轻膈肌萎缩,控制ICU呼吸机相关性肺炎。

Evolutionary Decision-Making and Planning for Autonomous Driving Based on Safe and Rational Exploration and Exploitation

Decision-making and motion planning are extremely important in autonomous driving to ensure safe driving in a real-world environment.This study proposes an online evolutionary decision-making and motion planning framework for autonomous driving based on a hybrid data-and model-driven method.First,a data-driven decision-making module based on deep reinforcement learning(DRL)is developed to pursue a rational driving performance as much as possible.Then,model predictive control(MPC)is employed to execute both longitudinal and lateral motion planning tasks.Multiple constraints are defined according to the vehicle’s physical limit to meet the driving task requirements.Finally,two principles of safety and rationality for the self-evolution of autonomous driving are proposed.A motion envelope is established and embedded into a rational exploration and exploitation scheme,which filters out unreasonable experiences by masking unsafe actions so as to collect high-quality training data for the DRL agent.Experiments with a high-fidelity vehicle model and MATLAB/Simulink co-simulation environment are conducted,and the results show that the proposed online-evolution framework is able to generate safer,more rational,and more efficient driving action in a real-world environment.

Escape room游戏宣教对阴道分娩初产妇分娩恐惧及产程进展的影响

目的探究Escape room游戏宣教对阴道分娩初产妇分娩恐惧及产程进展的影响。方法采用便利抽样法,选取本院2021年1月—2022年6月收治的140例阴道分娩初产妇为研究对象,按随机数字表法将其分为对照组和观察组,每组各70例。对照组采取常规教育模式,观察组在常规护理基础上应用Escape room游戏宣教,比较两组初产妇分娩恐惧水平、产程进展。结果观察组分娩恐惧中高水平初产妇占比为57.14%小于对照组的80.00%,差异有统计学意义(P<0.05);观察组初产妇第一产程时间、第二产程时间均短于对照组,差异有统计学意义(P<0.05),两组第三产程时间比较差异无统计学意义(P>0.05)。结论Escape room游戏宣教在阴道分娩初产妇中的应用,能缓解产妇分娩恐惧情绪,可一定程度上加快产程进展。

优化ESCAPE集束化策略对ICU亚临床谵妄患者的效果评价

目的 分析优化ESCAPE集束化策略对ICU亚临床谵妄患者的效果。方法 选取本院入住ICU超过24h的亚临床谵妄患者,对照组予常规护理,观察组在常规护理上给优化ESCAPE集束化策略。比较2组睡眠质量、认知水平、谵妄发生率及48h内亚临床谵妄持续时间。结果 观察组睡眠质量、认知水平、谵妄发生率、亚临床谵妄持续时间低于对照组,差异有统计学意义(P<0.05)。结论 优化ESCAPE集束化策略可提高患者睡眠质量,改善亚临床谵妄患者认知水平,缩短亚临床谵妄持续时间,降低谵妄发生率。

Correction:The escape mechanisms of the proto-atmosphere on terrestrial planets:“boil-off”escape,hydrodynamic escape and impact erosion

In the original publication of the article,the affiliation“College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing,People’s Republic of China”for author Ziqi Wang was missing and included in this correction article.

Toward Trustworthy Decision-Making for Autonomous Vehicles:A Robust Reinforcement Learning Approach with Safety Guarantees

While autonomous vehicles are vital components of intelligent transportation systems,ensuring the trustworthiness of decision-making remains a substantial challenge in realizing autonomous driving.Therefore,we present a novel robust reinforcement learning approach with safety guarantees to attain trustworthy decision-making for autonomous vehicles.The proposed technique ensures decision trustworthiness in terms of policy robustness and collision safety.Specifically,an adversary model is learned online to simulate the worst-case uncertainty by approximating the optimal adversarial perturbations on the observed states and environmental dynamics.In addition,an adversarial robust actor-critic algorithm is developed to enable the agent to learn robust policies against perturbations in observations and dynamics.Moreover,we devise a safety mask to guarantee the collision safety of the autonomous driving agent during both the training and testing processes using an interpretable knowledge model known as the Responsibility-Sensitive Safety Model.Finally,the proposed approach is evaluated through both simulations and experiments.These results indicate that the autonomous driving agent can make trustworthy decisions and drastically reduce the number of collisions through robust safety policies.

Orientation and Decision-Making for Soccer Based on Sports Analytics and AI:A Systematic Review

Due to ever-growing soccer data collection approaches and progressing artificial intelligence(AI) methods, soccer analysis, evaluation, and decision-making have received increasing interest from not only the professional sports analytics realm but also the academic AI research community. AI brings gamechanging approaches for soccer analytics where soccer has been a typical benchmark for AI research. The combination has been an emerging topic. In this paper, soccer match analytics are taken as a complete observation-orientation-decision-action(OODA) loop.In addition, as in AI frameworks such as that for reinforcement learning, interacting with a virtual environment enables an evolving model. Therefore, both soccer analytics in the real world and virtual domains are discussed. With the intersection of the OODA loop and the real-virtual domains, available soccer data, including event and tracking data, and diverse orientation and decisionmaking models for both real-world and virtual soccer matches are comprehensively reviewed. Finally, some promising directions in this interdisciplinary area are pointed out. It is claimed that paradigms for both professional sports analytics and AI research could be combined. Moreover, it is quite promising to bridge the gap between the real and virtual domains for soccer match analysis and decision-making.

When Fleeing Matters:Differences in Escape Behaviours of Three Northeast Asian Anurans

Prey species may have their own optimal escape strategy to balance predation risks and the energetic cost of fleeing.Some species have an advantage when maintaining a short fleeing distance,while others may favour an earlier escape based on microhabitat,size,or body condition.Here,we examined the escape behaviour of the three syntopic Northeast Asian anuran species:Mongolian toads(Strauchbufo raddei),Amur brown frogs(Rana amurensis),and Japanese treefrogs(Dryophytes japonicus)in Mongolia,Russia,China and DPR Korea.We examined flight initiation distance(FID;the distance from a potential predator to the point when the individual starts to flee)and distance fled(DF;distance between flight initiation and flight termination points)of each species and the effects of microhabitat,sex,and body size.Strauchbufo raddei and R.amurensis had a longer FID than D.japonicus,and S.raddei also had a longer DF than D.japonicus.These trends remained similar when dividing FID and DF by a size proxy(snout-vent length)for all individuals.This suggests that the treefrog D.japonicus used a strategy to stay immobile even when they were detected,and the toad S.raddei reacted quicker and more sensitively to predators despite the presence of toxin.Female S.raddei had a significantly longer FID than males suggesting that females are more sensitive to predation risk in this species,but body size was not significant for any of the three species.Our results indicate that the three sympatric species have different escaping strategies,likely related to differences in physiology and crypticity.

Ethical Decision-Making Framework Based on Incremental ILP Considering Conflicts

Humans are experiencing the inclusion of artificial agents in their lives,such as unmanned vehicles,service robots,voice assistants,and intelligent medical care.If the artificial agents cannot align with social values or make ethical decisions,they may not meet the expectations of humans.Traditionally,an ethical decision-making framework is constructed by rule-based or statistical approaches.In this paper,we propose an ethical decision-making framework based on incremental ILP(Inductive Logic Programming),which can overcome the brittleness of rule-based approaches and little interpretability of statistical approaches.As the current incremental ILP makes it difficult to solve conflicts,we propose a novel ethical decision-making framework considering conflicts in this paper,which adopts our proposed incremental ILP system.The framework consists of two processes:the learning process and the deduction process.The first process records bottom clauses with their score functions and learns rules guided by the entailment and the score function.The second process obtains an ethical decision based on the rules.In an ethical scenario about chatbots for teenagers’mental health,we verify that our framework can learn ethical rules and make ethical decisions.Besides,we extract incremental ILP from the framework and compare it with the state-of-the-art ILP systems based on ASP(Answer Set Programming)focusing on conflict resolution.The results of comparisons show that our proposed system can generate better-quality rules than most other systems.

Research on decision-making behavior of multi-agent alliance in cross-border electricity market environment: an evolutionary game

Constructing a cross-border power energy system with multiagent power energy as an alliance is important for studying cross-border power-trading markets.This study considers multiple neighboring countries in the form of alliances,introduces neighboring countries’exchange rates into the cross-border multi-agent power-trading market and proposes a method to study each agent’s dynamic decision-making behavior based on evolutionary game theory.To this end,this study uses three national agents as examples,constructs a tripartite evolutionary game model,and analyzes the evolution process of the decision-making behavior of each agent member state under the initial willingness value,cost of payment,and additional revenue of the alliance.This research helps realize cross-border energy operations so that the transaction agent can achieve greater trade profits and provides a theoretical basis for cooperation and stability between multiple agents.

Stroke Risk Assessment Decision-Making Using a Machine Learning Model:Logistic-AdaBoost

Stroke is a chronic cerebrovascular disease that carries a high risk.Stroke risk assessment is of great significance in preventing,reversing and reducing the spread and the health hazards caused by stroke.Aiming to objectively predict and identify strokes,this paper proposes a new stroke risk assessment decision-making model named Logistic-AdaBoost(Logistic-AB)based on machine learning.First,the categorical boosting(CatBoost)method is used to perform feature selection for all features of stroke,and 8 main features are selected to form a new index evaluation system to predict the risk of stroke.Second,the borderline synthetic minority oversampling technique(SMOTE)algorithm is applied to transform the unbalanced stroke dataset into a balanced dataset.Finally,the stroke risk assessment decision-makingmodel Logistic-AB is constructed,and the overall prediction performance of this new model is evaluated by comparing it with ten other similar models.The comparison results show that the new model proposed in this paper performs better than the two single algorithms(logistic regression and AdaBoost)on the four indicators of recall,precision,F1 score,and accuracy,and the overall performance of the proposed model is better than that of common machine learning algorithms.The Logistic-AB model presented in this paper can more accurately predict patients’stroke risk.

Research on Maneuver Decision-Making of Multi-Agent Adversarial Game in a Random Interference Environment

The strategy evolution process of game players is highly uncertain due to random emergent situations and other external disturbances.This paper investigates the issue of strategy interaction and behavioral decision-making among game players in simulated confrontation scenarios within a random interference environment.It considers the possible risks that random disturbances may pose to the autonomous decision-making of game players,as well as the impact of participants’manipulative behaviors on the state changes of the players.A nonlinear mathematical model is established to describe the strategy decision-making process of the participants in this scenario.Subsequently,the strategy selection interaction relationship,strategy evolution stability,and dynamic decision-making process of the game players are investigated and verified by simulation experiments.The results show that maneuver-related parameters and random environmental interference factors have different effects on the selection and evolutionary speed of the agent’s strategies.Especially in a highly uncertain environment,even small information asymmetry or miscalculation may have a significant impact on decision-making.This also confirms the feasibility and effectiveness of the method proposed in the paper,which can better explain the behavioral decision-making process of the agent in the interaction process.This study provides feasibility analysis ideas and theoretical references for improving multi-agent interactive decision-making and the interpretability of the game system model.

Determination of the best materials for development and designing product using a multi-criteria decision-making

Purpose–Material selection,driven by wide and often conflicting objectives,is an important,sometimes difficult problem in material engineering.In this context,multi-criteria decision-making(MCDM)methodologies are effective.An approach of MCDM is needed to cater to criteria of material assortment simultaneously.More firms are now concerned about increasing their productivity using mathematical tools.To occupy a gap in the previous literature this research recommends an integrated MCDM and mathematical Bi-objective model for the selection of material.In addition,by using the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS),the inherent ambiguities of decision-makers in paired evaluations are considered in this research.It goes on to construct a mathematical bi-objective model for determining the best item to purchase.Design/methodology/approach–The entropy perspective is implemented in this paper to evaluate the weight parameters,while the TOPSIS technique is used to determine the best and worst intermediate pipe materials for automotive exhaust system.The intermediate pipes are used to join the components of the exhaust systems.The materials usually used to manufacture intermediate pipe are SUS 436LM,SUS 430,SUS 304,SUS 436L,SUH 409 L,SUS 441 L and SUS 439L.These seven materials are evaluated based on tensile strength(TS),hardness(H),elongation(E),yield strength(YS)and cost(C).A hybrid methodology combining entropy-based criteria weighting,with the TOPSIS for alternative ranking,is pursued to identify the optimal design material for an engineered application in this paper.This study aims to help while filling the information gap in selecting the most suitable material for use in the exhaust intermediate pipes.After that,the authors searched for and considered eight materials and evaluated them on the following five criteria:(1)TS,(2)YS,(3)H,(4)E and(5)C.The first two criteria have been chosen because they can have a lot of influence on the behavior of the exhaust intermediate pipes,on their performance and on the cost.In this structure,the weights of the criteria are calculated objectively through the entropy method in order to have an unbiased assessment.This essentially measures the quantity of information each criterion contribution,indicating the relative importance of these criteria better.Subsequently,the materials were ranked using the TOPSIS method in terms of their relative performance by measuring each material from an ideal solution to determine the best alternative.The results show that SUS 309,SUS 432L and SUS 436 LM are the first three materials that the exhaust intermediate pipe optimal design should consider.Findings–The material matrix of the decision presented in Table 3 was normalized through Equation 5,as shown in Table 5,and the matrix was multiplied with weighting criteriaß_j.The obtained weighted normalized matrix V_ij is presented in Table 6.However,the ideal,worst and best value was ascertained by employing Equation 7.This study is based on the selection of material for the development of intermediate pipe using MCDM,and it involves four basic stages,i.e.method of translation criteria,screening process,method of ranking and search for methods.The selection was done through the TOPSIS method,and the criteria weight was obtained by the entropy method.The result showed that the top three materials are SUS 309,SUS 432L and SUS 436 LM,respectively.For the future work,it is suggested to select more alternatives and criteria.The comparison can also be done by using different MCDM techniques like and Choice Expressing Reality(ELECTRE),Decision-Making Trial and Evaluation Laboratory(DEMATEL)and Preference Ranking Organization Method for Enrichment Evaluation(PROMETHEE).Originality/value–The results provide important conclusions for material selection in this targeted application,verifying the employment of mutual entropy-TOPSIS methodology for a series of difficult engineering decisions in material engineering concepts that combine superior capacity with better performance as well as cost-efficiency in various engineering design.

The Spherical q-Linear Diophantine Fuzzy Multiple-Criteria Group Decision-Making Based on Differential Measure

Spherical q-linearDiophantine fuzzy sets(Sq-LDFSs)provedmore effective for handling uncertainty and vagueness in multi-criteria decision-making(MADM).It does not only cover the data in two variable parameters but is also beneficial for three parametric data.By Pythagorean fuzzy sets,the difference is calculated only between two parameters(membership and non-membership).According to human thoughts,fuzzy data can be found in three parameters(membership uncertainty,and non-membership).So,to make a compromise decision,comparing Sq-LDFSs is essential.Existing measures of different fuzzy sets do,however,can have several flaws that can lead to counterintuitive results.For instance,they treat any increase or decrease in the membership degree as the same as the non-membership degree because the uncertainty does not change,even though each parameter has a different implication.In the Sq-LDFSs comparison,this research develops the differentialmeasure(DFM).Themain goal of the DFM is to cover the unfair arguments that come from treating different types of FSs opposing criteria equally.Due to their relative positions in the attribute space and the similarity of their membership and non-membership degrees,two Sq-LDFSs formthis preference connectionwhen the uncertainty remains same in both sets.According to the degree of superiority or inferiority,two Sq-LDFSs are shown as identical,equivalent,superior,or inferior over one another.The suggested DFM’s fundamental characteristics are provided.Based on the newly developed DFM,a unique approach tomultiple criterion group decision-making is offered.Our suggestedmethod verifies the novel way of calculating the expert weights for Sq-LDFSS as in PFSs.Our proposed technique in three parameters is applied to evaluate solid-state drives and choose the optimum photovoltaic cell in two applications by taking uncertainty parameter zero.The method’s applicability and validity shown by the findings are contrasted with those obtained using various other existing approaches.To assess its stability and usefulness,a sensitivity analysis is done.

A NovelMethod for Determining Tourism Carrying Capacity in a Decision-Making Context Using q−Rung Orthopair Fuzzy Hypersoft Environment

Tourism is a popular activity that allows individuals to escape their daily routines and explore new destinations for various reasons,including leisure,pleasure,or business.A recent study has proposed a unique mathematical concept called a q−Rung orthopair fuzzy hypersoft set(q−ROFHS)to enhance the formal representation of human thought processes and evaluate tourism carrying capacity.This approach can capture the imprecision and ambiguity often present in human perception.With the advanced mathematical tools in this field,the study has also incorporated the Einstein aggregation operator and score function into the q−ROFHS values to supportmultiattribute decision-making algorithms.By implementing this technique,effective plans can be developed for social and economic development while avoiding detrimental effects such as overcrowding or environmental damage caused by tourism.A case study of selected tourism carrying capacity will demonstrate the proposed methodology.