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 theχ2 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.

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.

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.

Effects of drip and flood irrigation on carbon dioxide exchange and crop growth in the maize ecosystem in the Hetao Irrigation District,China

Drip irrigation and flood irrigation are major irrigation methods for maize crops in the Hetao Irrigation District,Inner Mongolia Autonomous Region,China.This research delves into the effects of these irrigation methods on carbon dioxide(CO_(2))exchange and crop growth in this region.The experimental site was divided into drip and flood irrigation zones.The irrigation schedules of this study aligned with the local commonly used irrigation schedule.We employed a developed chamber system to measure the diurnal CO_(2)exchange of maize plants during various growth stages under both drip and flood irrigation methods.From May to September in 2020 and 2021,two sets of repeated experiments were conducted.In each experiment,a total of nine measurements of CO_(2)exchange were performed to obtain carbon exchange data at different growth stages of maize crop.During each CO_(2)exchange measurement event,CO_(2)flux data were collected every two hours over a day-long period to capture the diurnal variations in CO_(2)exchange.During each CO_(2)exchange measurement event,the biological parameters(aboveground biomass and crop growth rate)of maize and environmental parameters(including air humidity,air temperature,precipitation,soil water content,and photosynthetically active radiation)were measured.The results indicated a V-shaped trend in net ecosystem CO_(2)exchange in daytime,reducing slowly at night,while the net assimilation rate(net primary productivity)exhibited a contrasting trend.Notably,compared with flood irrigation,drip irrigation demonstrated significantly higher average daily soil CO_(2)emission and greater average daily CO_(2)absorption by maize plants.Consequently,within the maize ecosystem,drip irrigation appeared more conducive to absorbing atmospheric CO_(2).Furthermore,drip irrigation demonstrated a faster crop growth rate and increased aboveground biomass compared with flood irrigation.A strong linear relationship existed between leaf area index and light utilization efficiency,irrespective of the irrigation method.Notably,drip irrigation displayed superior light use efficiency compared with flood irrigation.The final yield results corroborated these findings,indicating that drip irrigation yielded higher harvest index and overall yield than flood irrigation.The results of this study provide a basis for the selection of optimal irrigation methods commonly used in the Hetao Irrigation District.This research also serves as a reference for future irrigation studies that consider measurements of both carbon emissions and yield simultaneously.

Quantification of irrigation water transport processes in ZiZiphus jujuba garden using water stable isotopes

ZiZiphus jujuba,which is native to China,has become one of the main crops widely planted in the western Loess Plateau because of its drought and flood-tolerance,adaptability,and higher nutritional value of the fruit.The irrigation water infiltration in Z.jujuba gardens is complex,and understanding its mechanisms is essential for efficient water use and sustainable agriculture.This knowledge helps ensure the long-term success of jujuba cultivation.This paper describes a field experiment that investigates the infiltration process of irrigation water from Z.jujuba garden and quantifies the contribution of irrigation water to soil water at different depths using the MixSIAR model.According to the FC(Field water holding Capacity)of Z.jujuba,irrigation experiments with three volumes of 80%FC,60%FC,and 40%FC are set up in this study.The study finds that water retention is better in Z.jujuba garden soils with a higher proportion of coarse gravel in the soil particle composition.Soil water content exhibits a gradient change after irrigation,with deeper wetting front transport depth observed with increased irrigation water.Additionally,there is correlation between soil temperature and soil water content.The soil water in Z.jujuba garden generally exhibits a preferential flow signal in the 0-40 cm range.Below 40 cm,a piston flow pattern dominates.The rate of soil water infiltration increases with the amount of irrigation water.In the 0-40 cm range of the soil vertical profile,irrigation water was the main contributor to soil water.Z.jujuba demonstrated flexibility in water uptake,primarily absorbing soil water at depths of 0-40 cm.For optimal growth of Z.jujuba at this stage,40%FC irrigation is recommended.The results are expected to be valuable future irrigation practices and land use planning for Z.jujuba garden in arid zones,supporting sustainable agricultural development and water management.

Expert consensus on irrigation and intracanal medication in root canal therapy

Chemical cleaning and disinfection are crucial steps for eliminating infection in root canal treatment. However, irrigant selection or irrigation procedures are far from clear. The vapor lock effect in the apical region has yet to be solved, impeding irrigation efficacy and resulting in residual infections and compromised treatment outcomes.

Irrigation and nitrogen fertiliser optimisation in protected vegetable fields of northern China:Achieving environmental and agronomic sustainability

Globally,sub-optimal use of nitrogen (N) fertiliser and elevated N irrigation groundwater have led to high leached nitrate (NO_(3)^(–)) losses from protected vegetable field systems.Optimising fertiliser and irrigation management in different soil types is crucial to reduce future N loads from such systems.The present 4-year study examined leached N loads from lysimeter monitoring arrays set up across 18 protected vegetable system sites encompassing the dominant soil types of northern China.The treatments applied at each field site were:1) a high N and high irrigation input treatment (HNHI);2) a low N but high irrigation input treatment (LNHI) and 3) a low N with low irrigation input treatment (LNLI).Results showed that the mean annual leached total nitrogen loads from the HNHI,LNHI and LNLI treatments were 325,294 and 257 kg N ha^(–1) in the fluvo-aquic soil,114,100 and 78 kg N ha^(–1) in the cinnamon soil and 79,68 and 57 kg N ha^(–1) in the black soil,respectively.The N dissolved in irrigation water in the fluvo-aquic soil areas was 8.26-fold higher than in the cinnamon areas.A structural equation model showed that N fertiliser inputs and leaching water amounts explained 14.7 and 81.8%of the variation of leached N loads,respectively.Correspondingly,reducing irrigation water by 21.5%decreased leached N loads by 20.9%,while reducing manure N and chemical N inputs by 22 and 25%decreased leached N loads by only 9.5%. This study highlights that protected vegetable fields dominated by fluvo-aquic soil need management to curtail leached N losses in northern China.

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.

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.

Effect of Water Application Rate on Growth Parameters of Farro 44 Rice Grown in a Selected Irrigation Scheme in Niger State, Nigeria

Water and land are the necessary agricultural inputs, and both are scarce these days. This study aims to determine the effect of water application rate on selected planting and crop parameters of Farro 44 rice during dry season farming and its growth response. The randomised complete block design was employed for the Farro 44 rice variety, with each plot size 4 m2 (2 m × 2 m) for ease of monitoring. A 0.3 m bound space separated each plot. The crop spacing was 0.2 m × 0.3 m, 0.3 m × 0.3 m, and 0.3 m × 0.4 m, respectively, for the row-to-row and plant-to-plant distance. The data collected were statistically analysed. The height of the faro 44 variety of rice ranged between 35.50 cm to 44.00 cm for plots with 2 tillers per hill, while that of 4 and 6 tillers per hill ranged between 35.50 cm to 41.40 cm and 35.50 cm to 39.30 cm, respectively. Minimum damage of 2.32% was seen for plant hills of 2 tillers, while 9.21% and 11.89% were observed for tillers of 4 and 6, respectively. It was seen that plots with the highest spacing of 30 × 40 cm and tillers of 2 per hill were observed to perform better than those of the other plots within the experimental pots. Such plots had a maximum plant tiller of 37 when counted, with the height of the plants reaching 44 cm after 70 days of planting. In conclusion, farmers within the study area of the Kanko community in Niger State. Nigeria appears not to have any known knowledge of the soil they are cultivating and the water they use as a source of irrigation within the farming areas. It was further concluded that the rice crops would be produced maximally with minimal water application to the rice field.

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.

A study of the soil water potential threshold values to trigger irrigation of ‘Shimizu Hakuto’ peach at pivotal fruit developmental stages

Water management is an important practice that affects fruit size and quality.Effective implementation of irrigation scheduling requires knowledge of the appropriate indicators and thresholds,which are established manly based on the effects of water deficits on final fruit quality.Few studies have focused on the real-time effects of water status on fruit and shoot growth.To establish soil water potential (ψ_(soil)) thresholds to trigger irrigation of peach at pivotal fruit developmental stages,photogrammetry,^(13)C labelling,and other techniques were used in this study to investigate real-time changes in stem diameter,fruit projected area,net leaf photosynthetic rate (P_(n)),and allocation of photoassimilates to fruit under soil water potential conditions ranging from saturation to stress in 6-year-old Shimizu hakuto’peach.Stem growth,fruit growth,and P_n exhibited gradually decreasing sensitivity to water deficits during fruit developmental stages I,II,and III.Stem diameter growth was significantly inhibited whenψ_(soil)dropped to-8.5,-7.6,and-5.4 k Pa,respectively.Fruit growth rate was low,reaching zero when theψ_(soil)was-9.0 to-23.1,-14.9 to-21.4,and-16.5 to-23.3 k Pa,respectively,and P_ndecreased significantly when theψ_(soil)reached-24.2,-22.7,and-20.4 kPa,respectively.In addition,more photoassimilates were allocated to fruit under moderateψ_(soil)conditions (-10.1 to-17.0 k Pa) than under otherψ_(soil)values.Our results revealed threeψ_(soil)thresholds,-10.0,-15.0,and-15.0 kPa,suitable for triggering irrigation during stages I,II,and III,respectively.These thresholds can be helpful for controlling excessive tree vigor,maintaining rapid fruit growth and leaf photosynthesis,and promoting the allocation of more photoassimilates to fruit.

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.

Exploring the combination of biochar‐amended soil and automated irrigation technology for water regulation and preservation in green infrastructure

Biochar is a carbon sink material with the potential to improve water retention in various soils.However,for the long‐term maintenance of green infrastructure,there is an additional need to regulate the water contents in the covers to maintain vegetation growth in semiarid conditions.In this study,biochar‐amended soil was combined with subsurface drip irrigation,and the water preservation characteristics of this treatment were investigated through a series of one‐dimensional soil column tests.To ascertain the best treatment method specific to semiarid climatic conditions,the test soil was amended with 0%,1%,3%,and 5%biochar.Automatic irrigation devices equipped with soil moisture sensors were used to control the subsurface water content with the aim of enhancing vegetation growth.Each soil column test lasted 150 h,during which the volumetric water contents and soil suction data were recorded.The experimental results reveal that the soil specimen amended with 3%biochar is the most water‐saving regardless of the time cost.Soil with a higher biochar content(e.g.,5%)consumes a more significant amount of water due to the enhancement of the water‐holding capacity.Based on the experimental results,it can be concluded that the appropriate ratio can be determined within 1%–3%,which can reduce not only the amount of irrigated/used water but also the time cost.Such technology can be explored for water content regulation in green infrastructure and the development of barriers for protecting the environment around deep underground waste containment.

Irrigation and Thermal Buffering Using Mathematical Modeling

Two methods of irrigation,drip,and sprinkler were studied to determine the response of the Javits green roof to irrigation.The control study was dry unirrigated plots.Drip irrigation consisted of irrigation tubes running through the green roof that would water the soil throughout and sprinkler irrigation used a sprinkler system to irrigate the green roof from above.In all cases,the irrigated roofs had increased the soil moisture,reduced temperatures of both the upper and lower surfaces,reduced growing medium temperatures and reduced air temperatures above the green roof relative to the unirrigated roof.The buffered temperature fluctuations were also studied via air conditioner energy consumption.There was a 28%reduction in air conditioner energy consumption and a 33%reduction in overall energy consumption between dry and irrigated plots.Values of thermal resistance or S were determined for accuracy and for this study,there was little change which is ideal.A series of infra-red and thermal probe measurements were used to determine temperatures in the air and sedum.It was determined that the sprinkler irrigation did a better job than the drip irrigation in keeping cooler temperatures within the green roof.A Mann-Whitney U test was performed to verify the variation in moisture temperatures buffering energy consumption.By getting a p-value<0.05,it indicates that the model is accurate for prediction and medium temperatures were statistically different.

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.