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Identifying cause-effect relations among variables is a key step in the decision-making process. Whereas causal inference requires randomized experiments, researchers and policy makers are increasingly using observational studies to test causal hypotheses due to the wide availability of data and the infeasibility of experiments. The matching method is the most used technique to make causal inference from observational data. However, the pair assignment process in one-to-one matching creates uncertainty in the inference because of different choices made by the experimenter. Recently, discrete optimization models have been proposed to tackle such uncertainty; however, they produce 0-1 nonlinear problems and lack scalability. In this work, we investigate this emerging data science problem and develop a unique computational framework to solve the robust causal inference test instances from observational data with continuous outcomes. In the proposed framework, we first reformulate the nonlinear binary optimization problems as feasibility problems. By leveraging the structure of the feasibility formulation, we develop greedy schemes that are efficient in solving robust test problems. In many cases, the proposed algorithms achieve a globally optimal solution. We perform experiments on real-world data sets to demonstrate the effectiveness of the proposed algorithms and compare our results with the state-of-the-art solver. Our experiments show that the proposed algorithms significantly outperform the exact method in terms of computation time while achieving the same conclusion for causal tests. Both numerical experiments and complexity analysis demonstrate that the proposed algorithms ensure the scalability required for harnessing the power of big data in the decision-making process. Finally, the proposed framework not only facilitates robust decision making through big-data causal inference, but it can also be utilized in developing efficient algorithms for other nonlinear optimization problems such as quadratic assignment problems. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grant 2047094]. Supplemental Material: The online supplements are available at https://doi.org/10.1287/ijoc.2022.1226 .

COVID-19 is a worldwide pandemic that is caused by severe acute respiratory syndrome coronavirus (SAR-CoV-2). For the effect of this pandemic, the people of Bangladesh are suffering from unprecedented challenges of all ages. Coronavirus pandemic has hit the young mental health badly. The main purpose of this research was to investigate the mental health condition among young people during the COVID-19 pandemic in Bangladesh. In this study, a qualitative research method was used where twenty case studies were carried out to evaluate critical situations as well as the determinants of psychological health problems that young adults are facing. Result demonstrates that like other ages, young people are bound to stay at home during lockdown that causes a profound effect on their mental health. Due to COVID-19 young people are going through a variety of critical situations including financial hardship, conflict with family members, quarantine-related crisis, increasing pressure for marriage, extreme addiction to the virtual world, and addiction to different video games that threaten their psychological health, for example increasing suicidal tendency, loneliness, anxiety, depression, psychological trauma, low self-confidence anger, etc. Researchers have suggested some potential recommendations to reduce the psychological pressure of young people during pandemics.

Opioid Use Disorder (OUD) has reached an epidemic level in the US. Diversion of unused prescription opioids to secondary users and black market significantly contributes to the abuse and misuse of these highly addictive drugs, leading to the increased risk of OUD and accidental opioid overdose within communities. Hence, it is critical to design effective strategies to reduce the non-medical use of opioids that can occur via diversion at the patient level. In this paper, we aim to address this critical public health problem by designing strategies for the return and safe disposal of unused prescription opioids. We propose a data-driven optimization framework to determine the optimal incentive disbursement plans and locations of easily accessible opioid disposal kiosks to motivate prescription opioid users of diverse profiles in returning their unused opioids. We develop a Mixed-Integer Non-Linear Programming (MINLP) model to solve the decision problem, followed by a reformulation scheme using Benders Decomposition that results in a computationally efficient solution. We present a case study to show the benefits and usability of the model using a dataset created from Massachusetts All Payer Claims Data (MA APCD). Our proposed model allows the policymakers to estimate and include a penalty cost considering the economic and healthcare burden associated with prescription opioid diversion. Our numerical experiments demonstrate the ability of model and usefulness in determining optimal locations of opioid disposal kiosks and incentive disbursement plans for maximizing the disposal of unused opioids. The proposed optimization framework offers various trade-off strategies that can help government agencies design pragmatic policies for reducing the diversion of unused prescription opioids.

Background: The brand name Suboxone and its generic formulation buprenorphine/naloxone is a medication for treating opioid use disorder. While this medication has been shown to be effective, little research has examined the extent to which it is being prescribed and under what circumstances.Objective: This study examined patterns of prescription claims for buprenorphine/naloxone in terms of volume and associated clinical conditions.Methods: The study was conducted using a statewide database comprising pharmacy and medical claims that were covered by commercial health insurance plans in Massachusetts between 2011 and 2015. Trends in prescription volume for buprenorphine/naloxone were assessed based on the annual number of patients with a prescription for buprenorphine/naloxone. To examine clinical conditions associated with buprenorphine/naloxone prescriptions, patients' pharmacy claims were linked to their medical claims within the prior three months. For patients with common pain-related conditions, the odds they were prescribed buprenorphine/naloxone rather than oxycodone, a widely used opioid for pain management, were also examined.Results: The number of patients with a buprenorphine/naloxone prescription increased substantially during the study period, from approximately 25,000 in 2011 to over 39,000 in 2015. The most common clinical condition associated with buprenorphine/naloxone prescribing was opioid use disorder, but a substantial percentage of prescriptions were preceded by diagnoses that included pain or were for pain alone.Conclusion: A substantial increase in the number of patients with a prescription for buprenorphine/naloxone was observed. While buprenorphine/naloxone is most frequently prescribed for opioid use disorder, clinicians also appear to prescribe it for pain, particularly for patients who may be at elevated risk for opioid use disorder.

Policymakers, practitioners, and researchers around the globe have been acting in a coordinated manner, yet remaining independent, to achieve the seventeen Sustainable Development Goals (SDGs) defined by the United Nations. Remarkably, SDG-centric activities have manifested a huge information silo known as big data. In most cases, a relevant subset of big data is visualized using several two-dimensional plots. These plots are then used to decide a course of action for achieving the relevant SDGs, and the whole process remains rather informal. Consequently, the question of how to make a formal decision using big data-generated two-dimensional plots is a critical one. This article fills this gap by presenting a novel decision-making approach (method and tool). The approach formally makes decisions where the decision-relevant information is two-dimensional plots rather than numerical data. The efficacy of the proposed approach is demonstrated by conducting two case studies relevant to SDG 12 (responsible consumption and production). The first case study confirms whether or not the proposed decision-making approach produces reliable results. In this case study, datasets of wooden and polymeric materials regarding two eco-indicators (CO2 footprint and water usage) are represented using two two-dimensional plots. The plots show that wooden and polymeric materials are indifferent in water usage, whereas wooden materials are better than polymeric materials in terms of CO2 footprint. The proposed decision-making approach correctly captures this fact and correctly ranks the materials. For the other case study, three materials (mild steel, aluminum alloys, and magnesium alloys) are ranked using six criteria (strength, modulus of elasticity, cost, density, CO2 footprint, and water usage) and their relative weights. The datasets relevant to the six criteria are made available using three two-dimensional plots. The plots show the relative positions of mild steel, aluminum alloys, and magnesium alloys. The proposed decision-making approach correctly captures the decision-relevant information of these three plots and correctly ranks the materials. Thus, the outcomes of this article can help those who wish to develop pragmatic decision support systems leveraging the capacity of big data in fulfilling SDGs.

Renewable energy plants can participate in the energy pool market including day-ahead, intraday and balancing markets. The aim of this work is to develop a decision-making framework for a Wind and Storage Power Plant participating in the pool market to handle the uncertainty associated with the parameters of energy price and available wind energy, which are not known when decisions are to be made. Thus, the problem of maximizing the net income of such a plant participating in the pool market is formulated as a two-stage convex stochastic program. A novel hybrid approach using multivariate clustering technique and recurrent neural network is used to derive scenarios to handle the uncertainty associated with the energy price. Lastly, simulation experiments are carried out to show the effectiveness of the proposed methods using a real-world case study. Operators of variable renewable resource generators could use the proposed framework to make robust decisions and better manage their operations to gain competitive advantage.

Unexpected component failures in a mechanical system always cause loss of performance and functionality of the entire system. Condition-based maintenance decisions for a multi-component mechanical system are challenging because the interdependence of individual components’ degradation is not fully understood and lack of physical models. Most existing literature commonly assumes that degradation and failure of individual components within a mechanical system are independent, which could lead to inaccurate diagnostic and prognostic results. In this research, state-rate dependence denoting interaction between component health condition (degradation state) and failure rate is proposed for degradation and failure analysis for a two-component repairable system. A state discretization technique is proposed to model how health state of one component affects the hazard rate of another. An extended proportional hazard model (PHM) is used to characterize the failure dependence and estimate the influence of degradation state of one component on the hazard rate of another. An optimization model is developed to determine the optimal hazard-based threshold for a two-component repairable system. A case study on a generic industrial gearbox has been conducted to show the effectiveness of the proposed model.

Opioid overdose epidemic is a national public health crisis in the US. Little is known about how large-scale data analytics can be leveraged to help physicians predict whether a prescription opioid user will develop opioid use disorder. To that end, we proposed a machine learning framework for identifying potential risk factors of opioid use disorder from a large-scale healthcare claims data. These risk factors identified by the proposed framework can be used to predict which patient will be at higher risk of opioid use disorder following an opioid prescription. We utilized clinical diagnosis and prescription histories from Massachusetts commercially insured individuals who were prescribed opioids. We performed several feature selection techniques on a class imbalanced analytic sample to identify patient-level demographic and clinical features that were influential predictors of opioid use disorder. We, then compared the predictive power of four well-known machine learning algorithms: Logistic Regression, Random Forest, Decision Tree, and Gradient Boosting to predict the patients’ risk of opioid use disorder. The study results showed that the Random Forest model achieved superior predictive performance in terms of AUC and recall. Alongside the higher predictive accuracy, the random forest model identified clinical features, some of which were fairly consistent with prior clinical findings. In addition, our proposed framework is capable of extracting some other clinical features, which are predictive of opioid use disorder and indicative as the proxies of patients’ health status. We anticipate that the findings of our study will potentially help reduce in-appropriate and over prescription of opioids.

Background Research has shown buprenorphine/naloxone to be an effective medication for treating individuals with opioid use disorder. At the same time, treatment discontinuation rates are reportedly high though much of the extant evidence comes from studies of the Medicaid population. Objectives To examine the pattern and determinants of buprenorphine/naloxone treatment discontinuation in a population of commercially insured individuals. Research design We performed a retrospective observational analysis of Massachusetts All Payer Claims Data (MA APCD) covering years 2013 through 2017. We defined treatment discontinuation as a gap of 60 consecutive days without a prescription for buprenorphine/naloxone within a time frame of 24 months from the initiation of treatment. A mixed-effect Cox proportional hazard model examined the associated risk of discontinuing treatment with baseline predictors. Subjects A total of 5134 individuals who were commercially insured during the study period. Measures Buprenorphine/naloxone treatment discontinuation. Results Overall 75% of individuals had discontinued treatment within two years of initiating treatment, and median time to discontinuation was 300 days. Patients aged between 18 and 24 years (HR = 1.436, 95%, CI = 1.240–1.663) and receiving treatment from prescribers with high panel-size (HR = 1.278, 95% CI = 1.112–1.468) had higher risk of discontinuing treatment. On the contrary, patients receiving treatment from multiple prescribers had lower associated risk of treatment discontinuation. Conclusions A substantial percentage of patients discontinue treatment well before they can typically meet criteria for sustained remission. Further investigations should assess the clinical outcomes following premature discontinuation and identify strategies for retaining patients in treatment.

In this paper, we define a new, special second order cone as a type-$k$ second order cone. We focus on the case of $k=2$, which can be viewed as SOCO with an additional {\em complicating variable}. For this new problem, we develop the necessary prerequisites, based on previous work for traditional SOCO. We then develop a primal-dual interior point algorithm for solving a type-2 second order conic optimization (SOCO) problem, based on a family of kernel functions suitable for this type-2 SOCO. We finally derive the following iteration bound for our framework: \[\frac{L^\gamma}{\theta \kappa \gamma} \left[2N \psi\left( \frac{\varrho \left(\tau /4N\right)}{\sqrt{1-\theta}}\right)\right]^\gamma\log \frac{3N}{\epsilon}.\]

Decisions for a variable renewable resource generator’s commitment in the energy market are typically made in advance when little information is obtainable about wind availability and market prices. Much research has been published recommending various frameworks for addressing this issue. However, these frameworks are limited as they do not consider all markets a producer can participate in. Moreover, current stochastic programming models do not allow for uncertainty data to be updated as more accurate information becomes available. This work proposes two decision-making frameworks for a wind energy generator participating in day-ahead, intraday, reserve, and balancing markets. The first framework is a two-stage stochastic convex optimization approach, where both scenario-independent and scenario-dependent decisions are made concurrently. The second framework is a series of four two-stage stochastic optimization models wherein the results from each model feed into each subsequent model allowing for scenarios to be updated as more information becomes available to the decision-maker. In the simulation experiments, the multi-phase framework performs better than the single-phase in every run, and results in an average profit increase of 7%. The proposed optimization frameworks aid in better decision-making while addressing uncertainty related to variable resource generators and maximize the return on investment.

In prior literature regarding facility location problems, there has been little explicit acknowledgement of problems arising from concave (non-convex) regions. This issue extends to computational geometry as a whole, as there is a distinct deficiency in existing center finding techniques amidst work on forbidden regions. In this paper, we present a novel method for finding representative regional center-points, referred to as “Concave Interior Centers”, to approximate inter-regional distances for solving optimal facility location problems. The validity of the proposal as a means for solving these placements is discussed on three “special cases”, and on a humanitarian focused real-world application. We compare the performance of the Concave Interior Center to the results from using Geometric Centers. We discuss the implications of using externally located representative centers in facility location problems. The context of the application involves maximizing the potential services available to homeless persons in Fairfield County, Connecticut under a given budget through the construction of limited capacity night-by-night shelters and optionally included food pantries. Our computational results show the efficiency of the proposed techniques in solving a critical societal problem.

Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same data set, using a seemingly identical procedure, only to find a different conclusion. However, as we show in this work, there is a typical source of uncertainty that is essentially never considered in observational causal studies: the choice of match assignment for matched groups—that is, which unit is matched to which other unit before a hypothesis test is conducted. The choice of match assignment is anything but innocuous and can have a surprisingly large influence on the causal conclusions. Given that a vast number of causal inference studies test hypotheses on treatment effects after treatment cases are matched with similar control cases, we should find a way to quantify how much this extra source of uncertainty impacts results. What we would really like to be able to report is that no matter which match assignment is made, as long as the match is sufficiently good, then the hypothesis test results are still informative. In this paper, we provide methodology based on discrete optimization to create robust tests that explicitly account for this possibility. We formulate robust tests for binary and continuous data based on common test statistics as integer linear programs solvable with common methodologies. We study the finite-sample behavior of our test statistic in the discrete-data case. We apply our methods to simulated and real-world data sets and show that they can produce useful results in practical applied settings. History: Galit Shmueli served as the senior editor for this article. Funding: Financial support from the Natural Sciences and Engineering Research Council of Canada and the National Science Foundation [Grant IIS 2147061] is gratefully acknowledged. Data Ethics & Reproducibility Note: No data ethics considerations are foreseen related to this paper. Code and data to reproduce all the results in this paper are avilable at https://github.com/marcomorucci/robusttests and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2022.0020 ).

During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks. One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them to the affected people. To successfully deliver these items to the people in need, the organization needs to make decisions that range from the quick acquisition of vehicles from the local market, to the preparation of pickup and delivery schedules and vehicle routes. During crises, the supply of vehicles is often limited, their acquisition cost is steep, and special rental periods are imposed. At the same time, the affected area needs the aid materials as fast as possible, and deliveries must be made within due time. Therefore, it is imperative that the decisions of acquiring, scheduling, and routing of vehicles are made optimally and quickly. In this paper, we consider a variant of a truckload open vehicle routing problem with time windows, which is suitable for modeling vehicle routing operations during a humanitarian crisis. We present two integer linear programming models to formulate the problem, with the first one being an arc-based mixed integer linear programming model. The second model is a path-based integer linear programming model, for which we design two fast path generation algorithms. The first model is solved exactly using the commercial solver, while we propose to solve the second model within a column generation framework. Finally, we perform numerical experiments and compare the results obtained from the two models. We show that the path-based model, when solved with our column generation algorithm, outperforms the arc-based model in terms of solution time without sacrificing the solution quality.

In condition-based maintenance, preventive replacement threshold and inspection scheme play important roles in maintenance performance. Major research considers cost as the main objective for measuring maintenance performance; here the average cost per unit time is used as the only objective in a single-unit system. The intention of this study was to investigate that how the average cost per unit time varies through changing replacement threshold and inspection scheme, the aim is to simultaneously determine an optimal replacement threshold and inspection scheme. The heterogeneity of hazard rate over stages of the equipment entails less frequent inspections when the equipment is at a healthy condition and more frequent inspections when the equipment is at a progressively deteriorated condition. Therefore the proposed condition-based inspection in the present work is non-periodic. A method based on dynamic programming is developed in order to implement a condition-based inspection scheme; furthermore the threshold for preventive replacement and the inspection scheme are simultaneously determined and then the optimal average maintenance cost is obtained.

Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal Affine Scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we integrate Nesterov’s restarting strategy in the primal Affine Scaling method with an extra parameter, which in turn generalizes the original primal Affine Scaling method. We provide the proof of convergence for the proposed generalized algorithm considering long step size. We also provide the proof of convergence for the primal and dual sequence without the degeneracy assumption. This convergence result generalizes the original convergence result for the Affine Scaling methods and it gives us hints about the existence of a new family of methods. Then, we introduce a second algorithm to accelerate the convergence rate of the generalized algorithm by integrating a non-linear series transformation technique. Our numerical results show that the proposed algorithms outperform the original primal Affine Scaling method.

Healthcare facility location decisions are of great importance due to their impact on direct and social cost of people's well-being in a region. Optimal location decisions considering only current demand may become suboptimal as demand distribution changes. Considering future demand realisations in the decision making process can ensure long-term optimality. We present three mathematical models which follow grid-based location approach, and consider current and future demands in providing optimal location-allocation decisions. The first model considers allocations of present and future patients only to the nearest facilities. The second model allows patients to travel to facilities within allowable distance. The third model allows allocation of patients from one location to multiple facilities. The models are implemented with AMPL and numerical instances are solved with the CPLEX solver. Results show that the models are capable of solving medium size problems and the third model performs better in providing high quality solutions.

Supplier selection problem has gained extensive attention in the prior studies. However, research based on Fuzzy Multi-Attribute Decision Making (F-MADM) approach in ranking resilient suppliers in logistic 4.0 is still in its infancy. Traditional MADM approach fails to address the resilient supplier selection problem in logistic 4.0 primarily because of the large amount of data concerning some attributes that are quantitative, yet difficult to process while making decisions. Besides, some qualitative attributes prevalent in logistic 4.0 entail imprecise perceptual or judgmental decision relevant information, and are substantially different than those considered in traditional suppler selection problems. This study develops a Decision Support System (DSS) that will help the decision maker to incorporate and process such imprecise heterogeneous data in a unified framework to rank a set of resilient suppliers in the logistic 4.0 environment. The proposed framework induces a triangular fuzzy number from large-scale temporal data using probability-possibility consistency principle. Large number of non-temporal data presented graphically are computed by extracting granular information that are imprecise in nature. Fuzzy linguistic variables are used to map the qualitative attributes. Finally, fuzzy based TOPSIS method is adopted to generate the ranking score of alternative suppliers. These ranking scores are used as input in a Multi-Choice Goal Programming (MCGP) model to determine optimal order allocation for respective suppliers. Finally, a sensitivity analysis assesses how the Supplier's Cost versus Resilience Index (SCRI) changes when differential priorities are set for respective cost and resilience attributes.

Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.

Many problems in business, engineering, defence, resource exploitation, and even the medical sciences with location aspects can be expressed as grid-based location problems (GBLPs), modeled as integer linear programming problems. Such problems are often very computationally complex to solve. We develop a relax-and-fix-based decomposition approach to solve large-scale GBLPs, which we demonstrate will significantly reduce solution runtimes while not severely impacting optimality. We also introduce problem-specific logical restrictions, constraints that reduce the feasible region and the resulting branch-and-bound tree with minimal reductions in optimality.

Selecting optimal location is a key decision problem in business and engineering. This research focuses to develop mathematical models for a special type of location problems called grid-based location problems. It uses a real-world problem of placing lights in a park to minimize the amount of darkness and excess supply. The non-linear nature of the supply function (arising from the light physics) and heterogeneous demand distribution make this decision problem truly intractable to solve. We develop ILP models that are designed to provide the optimal solution for the light post problem: the total number of light posts, the location of each light post, and their capacities (i.e., brightness). Finally, the ILP models are implemented within a standard modeling language and solved with the CPLEX solver. Results show that the ILP models are quite efficient in solving moderately sized problems with a very small optimality gap.

Inherent complexity and uncertainty in a business environment necessitate the participation of many experts in multi criteria decision making. However, participation of many experts makes the conflict aggregation process difficult. To handle this difficulty, we propose two algorithms namely possibility measure and averaging conflict aggregation. In possibility measure, we integrate the possibility theory of fuzzy logic with a maximal containment method that is designed based on the decision problem. Possibility measure algorithm for ME-MCDM involves computationally expensive multiple information processing steps. Therefore to test and compare this algorithm, averaging conflict aggregation algorithm is proposed that requires fewer mathematical information processing steps. Based on the proposed algorithms, a decision support system (DSS) is developed. We present a case study of supplier evaluation to compare both of the proposed algorithms with the help of developed DSS.

This study compares nationwide medical and surgical readmission rates in patients with and without serious mental illness.

p-cycle networks have attracted a considerable interest in the network survivability literature in recent years. However, most of the existing work assumes a known network topology upon which to applyp-cycle restoration. In the present work, we develop an incremental topology optimization ILP forp-cycle network design, where a known topology can be amended with new fibre links selected from a set of eligible spans. The ILP proves to be relatively easy to solve for small test case instances but becomes computationally intensive on larger networks. We then follow with a relaxation-based decomposition approach to overcome this challenge. The decomposition approach significantly reduces computational complexity of the problem, allowing the ILP to be solved in reasonable time with no statistically significant impact on solution optimality.

In multi-stage project investment decision-making with uncertainty, risk mitigation plays a vital role. The return on investment (ROI) that will be realised in making a particular decision quite often carries a high degree of uncertainty, with an increased number of competing investors entering to the market every day. In this research, our objective is to develop a technique for a multi-stage project investment decision problem that deals with uncertainty in ROI and complex interrelated state transition dynamics. We do this by formulating our problem as an infinite horizon stochastic dynamic programming (IHSDP) problem and solve it to maximise the total return over an infinite time horizon. We have implemented our solution to the project investment decision problem in a simple case study using three well-known stochastic dynamic programming algorithms. Our simulation results show that the IHSDP algorithms are useful in making optimum investment decisions in an uncertain business environment.

Inherent complexity and uncertainty in a business environment necessitates the consideration of conflicting multi criteria in the supplier evaluation process. In multi criteria supplier evaluation process, there are many decision situations in which the information cannot be assessed precisely in a quantitative form but may be in a qualitative one. This research aims to develop a computing tool which can evaluate the supplier by taking the opinion of expert as a linguistic value in a fuzzy form and incorporating the uncertainty measure. The use of linguistic labels makes expert judgement more reliable and informative for decision making. To address the uncertainty during decision making, Alpha-cut which is a fuzzy algebra, shall be used to get a crisp range from a fuzzy range. To enlighten the effects of uncertainty, objective of this research is to perform a sensitivity analysis using the range of truth-value using alpha-cut and see how the decision is affected.