Stochastic Multicriteria Acceptability Analysis Research Articles

On the sigma-mu stochastic multicriteria analysis: Exact solutions for common particular cases

The sigma-mu approach is one of the recent innovations in the field of multicriteria decision aiding and composite indicators, extending the stochastic multicriteria acceptability analysis (SMAA) toolbox. The initial stage of this method involves computing the mean (mu) and standard deviation (sigma) for the composite value of the units under evaluation, considering a stochastic distribution on a set of admissible weights. This work develops closed-form formulas to obtain exact values for mu and sigma without needing approximations via Monte-Carlo simulations, which can be applied in some cases that are quite common. In terms of aggregation, these cases are characterized by an additive model, such as a weighted sum, a multiattribute value function, or PROMETHEE II. In terms of stochastic distributions, these cases include uniformly distributed unconstrained vectors of weights, rank-ordered vectors of weights, or lower-bounded weights. The developed formulas are applied to a didactic example and some open problems for future research are suggested.

Stochastic multi-attribute group decision-making for long-term comprehensive operation of cascade reservoirs under multiple uncertainties

Study regionThe Three Gorges cascade (TGC) reservoirs, China. Study focusSince uncertainties inherent in inflow forecasting, elevation-storage, discharge capacity, flood routing, and the preferences of decision makers (DMs) persist in the attribute measurements (AMs) and weights (AWs), problems where multiple DMs select the best compromise scheme for the long-term comprehensive operation of cascade reservoirs considering numerous attributes become a stochastic multi-attribute group decision-making (MAGDM) process. To represent uncertain AMs and AWs and consider the bounded rationality of DMs, we propose a stochastic MAGDM with integrated stochastic multicriteria acceptability analysis (SMAA) and gray cumulative prospect theory (GCPT), namely, SMAA-GCPT. After quantifying the uncertainties, SMAA-GCPT is used to model uncertain AMs and imperfect AWs with calculable probability distributions and map the sampled AMs and AWs to utility values to reflect the overall performance assuming bounded rationality. New hydrological insights for the regionExperiments on the TGC indicate that SMAA-GCPT can effectively differentiate alternative schemes and select the best compromise scheme to harmonize the conflicting benefits and risks of the TGC, with higher reliability than SMAA-2 and SMAA-GRA. The influence of uncertain AMs on the reliability of SMAA-GCPT is more obvious than that of uncertain AWs. The decision-making error risk is primarily sensitive to the inflow forecasting uncertainty, followed by the flood routing uncertainty, and is less affected by the uncertainties in elevation-storage and discharge capacity curves.

Stochastic multi-criteria decision-making for scheduling of wind–photovoltaic–hydropower systems

Abstract The decision-making process of wind–photovoltaic–hydropower systems involves knowledge from many fields. Influenced by the knowledge level of the decision-maker and the attribute information of the scheme set, there exists a certain uncertainty in the indicator weights. In view of this, this paper proposes a stochastic multi-criteria decision-making framework for scheduling of wind–photovoltaic–hydropower systems, which overcomes the difficulty of uncertainty in indicator weights or even completely unknown information about indicator weights at the time of decision-making. The Stochastic Multi-criteria Acceptability Analysis (SMAA) theory and the VIKOR model are introduced, and the proposed SMAA–VIKOR model makes the indicator weight space explicit. The study shows that the proposed SMAA–VIKOR model can overcome the obstacle of decision-makers’ lack of information on indicator weights. The ranking acceptability indicators calculated by the model show a more obvious trend of advantages and disadvantages, which gives full confidence to the decision-making group to formulate a plan to be implemented. It breaks through the bottleneck of group decision-making, which is difficult to make effective decisions due to the condition of incomplete information, and enriches the library of stochastic multi-criteria decision-making methods for the scientific formulation of scheduling schemes of wind–photovoltaic–hydropower systems under uncertainty conditions.

An approach to the integral optimization of investment portfolios

A comprehensive approach to the optimization of financial portfolios is provided by the Integral Analysis Method (IAM), which comprises four steps: The description of the problem is followed by three mathematical steps, namely, cardinal analysis, ordinal analysis and integration analysis, which allow simultaneously involving ordinal and cardinal variables in an optimization problem. The cardinal analysis uses the L_1 risk model, which is enriched by the inclusion of a stochastic constraint on the successful performance forecast attributed to each of the shares that make up the investment portfolio. This bound, however, does not alter the linear nature of the model. The Ordinal analysis includes expert opinions on the reputation of each company as a qualitative criterion. This completes two of the most relevant aspects of the investment portfolio optimization problem: success probability (assessed through the cardinal analysis) and business reputation (assessed through the ordinal analysis). By resorting to Stochastic Multicriteria Acceptability Analysis, the integration analysis allows obtaining indicators that jointly evaluate the variables resulting from the two previous analyses. As a validation process, IAM was applied to simulated data.

Incorporating Prior Data in Quantitative Benefit-Risk Assessments: Case Study of a Bayesian Method.

Multiple criteria decision analysis (MCDA) and stochastic multi-criteria acceptability analysis (SMAA) in their current implementation cannot incorporate prior or external information on benefits and risks. We demonstrate how to incorporate prior data using a Bayesian mixture model approach while conducting quantitative benefit-risk assessments (qBRA) for medical products. We implemented MCDA and SMAA in a Bayesian framework. To incorporate information from a prior study, we use mixture priors on each benefit and risk attribute that mixes information from a previous study with a vague prior distribution. The degree of borrowing is varied using a mixing proportion parameter. A demonstration case study for qBRA using the supplementary New Drug Application (sNDA) filing for Rivaroxaban for the indication of reduction in the risk of major thrombotic vascular events in patients with peripheral artery disease (PAD) was used to illustrate the method. Net utility scores, obtained from the randomized controlled trial data to support the sNDA, from the MCDA for Rivaraxoban and comparator were 0.48 and 0.56, respectively, with Rivaroxaban being the preferred alternative only 33% of the time. We show that with only 30% borrowing from a previous RCT, the MCDA and SMAA results are favorable for Rivaroxaban, accounting for the seemingly aberrant results on all-cause death in the trial data used to support the sNDA. Our method to formally incorporate prior data in MCDA and SMAA is easy to use and interpret. Software in the form of an RShiny App is available here: https://sai-dharmarajan.shinyapps.io/BayesianMCDA_SMAA/ .

Stochastic group preference acceptability analysis for interval-valued multiplicative preference relations based on TODIM method

Among many decision problems, interval-valued multiplicative preference relation (IMPR) is widely utilized due to its ability to express uncertain information. A new approach to solve group decision making (GDM) with IMPRs is proposed in this paper, named stochastic group preference acceptability analysis with TODIM (SGPAA-TODIM) method, by combining TODIM method (an acronym in Portuguese of Interactive and multi-criteria Decision Making) with stochastic multi-criteria acceptability analysis (SMAA-2). It effectively circumvents information loss and considers the weight and risk preferences of experts. Firstly, the stochastic multiplicative preference relation is defined through stochastic simulation employing a certain density function, and its priority weight vector is determined using the logarithmic least squares method (LLSM). Then, the priority preference comprehensive matrix is proposed by extracting information of priority vectors. Moreover, the novel SGPAA-TODIM method is developed to analyze the stochastic parameter spaces, with the optimal rank determined based on the analysis of acceptability degrees associated with dominance rank. Finally, to demonstrate the validity and applicability of the proposed method, numerical examples are given.

The SMAA-MABAC approach for healthcare supplier selection in belief distribution environment with uncertainties

Supplier selection is critical to the healthcare industry, especially in emergencies. Accurate and timely supply of healthcare resources can reduce economic cost and ensure the safety of people’s lives. However, the healthcare supplier market is enormous and complex; making accurate evaluations of different suppliers and helping managers choose the most suitable one when considering many factors is becoming an important task. Many multicriteria decision-making (MCDM) methods have been applied to supplier selection in existing literature. However, the research on healthcare supplier selection still needs to be completed. In this paper, to deal with healthcare supplier selection problems when there is no sufficient time and information to decide with uncertainty, the stochastic multicriteria acceptability analysis (SMAA) method and multi-attributive border approximation area comparison (MABAC) method are first combined by taking both the advantages of SMAA and MABAC methods when the assessments are expressed by belief distributions (BDs). In the SMAA-MABAC method, the global ignorance in BDs and the uncertain criteria weights are considered by judging the feasible space to derive the final rank of healthcare suppliers with the most possible. The more straightforward calculation process of SMAA-MABAC makes it faster to make an accurate choice among various suppliers. Moreover, it is flexible to generate different recommended suggestions when diverse preference information is added in SMAA-MABAC. Finally, a case study of healthcare supplier selection is examined for managers based on distributed reviews, and targeted selection advice is given concerning different demands. Besides, the sensitive analysis is provided to better understand the influence of the criteria weights on the proposed model. The results of the comparative analysis also show the effectiveness and rationality of the proposed method.

Integrated stochastic multicriteria acceptability analysis and data envelopment analysis with fixed-sum outputs: an application for evaluating participating nations in the Winter Olympics Games

Along with the popularity of Olympic Games, evaluating and ranking participating nations has become one of the hottest issues in recent years. Data envelopment analysis (DEA) is extensively used for participating nations’ performance evaluation, while the prior literature mainly addresses the maximum efficiency by ignoring the weights diversity, which might lead to unreasonable and biased results. By considering the fixed-sum medals constraint, this paper proposes an integrated approach of stochastic multicriteria acceptability analysis (SMAA) and DEA for evaluating the participating nations. The proposed approach addresses the weights diversity and multiple equilibrium efficient frontiers by investigating the overall feasible space, and two strategies are considered to guarantee the fairness concern for calculating the efficiencies. Besides, the proposed approach provides both rank acceptability and holistic acceptability index to obtain the complete ranking from the best to the worst and to get the relative ranking relationship in the overall feasible space. The proposed approach can provide more reasonable performance measurements since it explores different rank positions and improves the whole satisfaction of all participating nations. Finally, the proposed approach is applied to empirically analyze the participating nations in the Winter Olympic Games from 2010 to 2022 and some valuable analytical results are provided.

Inducing a probability distribution in Stochastic Multicriteria Acceptability Analysis

In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible value functions, and providing a final recommendation on the problem at hand considering only one of them could be considered arbitrary to some extent. For such a reason, Stochastic Multicriteria Acceptability Analysis gives information in statistical terms by taking into account a sample of models compatible with the provided preferences. These statistics are given assuming the existence of a probability distribution in the space of value functions being defined a priori. In this paper, we propose some methods aiming to build a probability distribution on the space of value functions considering the preference information given by the Decision Maker. To prove the goodness of our proposal we performed an extensive set of simulations. Moreover, a sensitivity analysis on the variables of our procedure has been done.

Unveiling the Decision-Making Dilemmas in Mini-Grids: The Intricate Case of Smart Meters

Mini-grids need to imitate the transition path of a traditional grid to maintain their position as a sustainable energy access alternative, while aligning with the objectives of the seventh Sustainable Development Goal. One such strategy is implementing smart-metering solutions to improve business viability and remote monitoring of distributed mini-grid assets. However, selecting smart meters presents a significant challenge for mini-grid operators, primarily due to the installation costs involved and the complexities associated with operating mini-grids in rural areas. Against this backdrop, the current case study’ demonstrates the utility of multi-criteria decision aids, such as stochastic multi-criteria acceptability analysis (SMAA), to assist mini-grid operators in making informed decisions concerning smart-meter selection. In addition, practitioners’ narratives elucidate how implementing smart metering can function as part of mini-grid operations in rural areas. Furthermore, narratives highlight the importance of considering context-specific conditions to avoid the under-utilisation of smart meters.

Multi-agent collaborative conceptual design method for robotic manufacturing systems in small- and mid-sized enterprises

Robotic manufacturing systems are essential in the post-pandemic world owing to their high level of flexibility and automation during a labor crisis. However, designing a suitable robotic manufacturing system for small- and mid-sized enterprises (SMEs) is challenging, considering both their financial burdens and the current supply chain disruptions of component suppliers. To address these challenges, this study proposes a distributed multi-agent collaborative conceptual design method involving designers and suppliers to assist SMEs in implementing robotic manufacturing systems. First, we propose a common data model that enables knowledge interaction between different agents during collaborative conceptual design. Subsequently, based on the proposed data model, the agent-based collaborative conceptual design process is developed, which enables different agents to communicate, interact, and negotiate with each other according to their experiences and knowledge. Third, an integrative algorithm based on 2-additive fuzzy measures, Choquet integral, and stochastic multi-criteria acceptability analysis is implemented to support the multi-agent decision-making process to robustly select architecture alternatives. As a case study, a real industrial design project of a robotic manufacturing system required by our industrial partner, is adopted to demonstrate the effectiveness of the proposed method.

Sentiment analysis of online reviews for electric vehicles using the SMAA-2 method and interval type-2 fuzzy sets

Numerous electric vehicles (EVs) consumers express their opinions about EVs on automotive websites. These online reviews can be mined and analyzed to understand consumer sentiment and preferences. Although the existing sentiment analysis (SA) has made insight into sentiment polarity of EVs, the SA results on different EV attributes do not consider the accuracy of sentiment classification and the difficulty of accurately obtaining attribute weights in the process of all attribute information fusion. To address these issues, we provide an integrated framework for the EV SA problem using the stochastic multi-criteria acceptability analysis (SMAA) method with interval type-2 fuzzy sets (IT2FSs). We first use a logistic regression model to classify the sentiment polarity for each online comment and construct IT2FS by sentiment classification accuracy to represent the SA results for different EV attributes. Based on this, we considered all feasible weights in the weight space and utilize the SMAA-IT2FS method to aggregate SA results and achieve EV ranking. In addition, our approach provide decision makers with information to assist in decision-making such as the use of central weight vectors to identify the strengths and weaknesses of EVs and the analysis of potential competitors through dominance relationships. Finally, real data extracted from AutoHome websites are used as experimental data to illustrate the implementation of the proposed method and to demonstrate the effectiveness of our approach.

A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information

Uncertainties are often present in typical portfolio decision analysis (PDA), and it is prudent to conduct a robust PDA to identify project portfolios that perform reasonably well across the entire range of uncertain parameter values. Previous research on robust PDA and applications has almost entirely relied on additive portfolio preference functions, with little research on robustness under multilinear portfolio utility functions (PUFs). A ranking approach for robust PDA is proposed based on multilinear PUFs, incomplete preference information, and the algorithm for accelerating stochastic multicriteria acceptability analysis (SMAA). First, the initial set of portfolios is screened through various constraints to produce a smaller set of desirable portfolios. Second, several types of incomplete preference information are thought to be elicited with regard to multilinear PUFs, including preference information on coefficients, portfolios, and uncertainties on preference elicitation techniques. Third, the SMAA decomposition algorithm is implemented as a ranking approach to perform robust PDA on the basis of multilinear PUFs, incomplete preference information, and potentially numerous portfolios in the set of desirable portfolios. Finally, the approach is applied to a case to validate its effectiveness, and comparisons among additive, multiplicative, and multilinear PUFs in terms of decision recommendations are performed.

Scoring from pairwise winning indices

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another. They are computed taking into account all the instances of the assumed preference model compatible with the preference information provided by the Decision Maker mainly, but not exclusively, in terms of pairwise preference comparisons of reference alternatives. In this paper we present a new scoring method assigning a value to each alternative summarizing the results of the pairwise winning indices. Several procedures of this type have been provided in literature. However, our method, expressing the score in terms of a representative additive value function, permits to disaggregate the overall evaluation of each alternative in the sum of contributions of considered criteria. This permits not only to rank the alternatives but also to explain the reasons for which an alternative obtains its evaluation and, consequently, fills a certain ranking position. We also present a probabilistic model underlying our methodology. This probabilistic model is based on a simple piecewise linear approximation of the cumulative normal distribution, which allows the use of linear programming. To prove the efficiency of the method in representing the preferences of the Decision Maker, we performed an extensive set of simulations varying the number of alternatives and criteria. The results of the simulations, analyzed from a statistical point of view, prove the reliability of our procedure. The applicability of the method to decision making problems is explained by means of a case study related to the evaluation of financial funds.

Consensus reaching in multi-criteria social network group decision making: A stochastic multicriteria acceptability analysis-based method

Multi-criteria social network group decision making (SNGDM) that allows decision makers (DMs) to interact with each other has attracted increasing attention in the field of decision analysis. In this paper, we take stochastic multicriteria acceptability analysis (SMAA) into account to study consensus reaching processes in multi-criteria SNGDM problems with manipulative behaviors. First, we propose a SMAA-based method to transform decision matrices into fuzzy preference relations to detect manipulators in multi-criteria SNGDM. Then, we design a new consensus determining mechanism using the weight stability interval and SMAA methods, which does not require a consensus threshold to be determined in advance. Based on this, we propose a two-stage feedback process to help DMs reach consensus. Then, we propose an algorithm to summarize the main steps of the proposed method. Finally, we use a case study of nursing home location selection to illustrate the effectiveness of the proposed method.

Stochastic multi-criteria decision making framework based on SMAA-VIKOR for reservoir flood control operation

ABSTRACT In reservoir flood control operation, candidate reservoir operation alternatives are evaluated, ranked and selected by a multi-criteria decision making (MCDM) method. However, deterministic methods cannot handle MCDM problems where uncertainties exist in both criteria performance values (PVs) and criteria weights (CWs). To solve the issue, a SMAA-VIKOR model integrating stochastic multicriteria acceptability analysis (SMAA) theory with the Viekriterijumsko Kompromisno Rangiranje (VIKOR) method is established based on Aydogan and Ozmen (2017). Moreover, we conduct a comprehensive evaluation of the model’s decision making results, including risk assessment and sensitivity analysis. The case study applied to a flood control system in Dadu River in China indicates that the SMAA-VIKOR model can quickly identify the optimal alternative that meets the subjective preferences of decision makers, and has remarkable advantages compared to the traditional SMAA-2 model and the deterministic VIKOR method, which can provide theoretical support for making a robust reservoir release decision.

POLITICAL RISK: INTERPRETING THE INTERNATIONAL CONTEXT.

Introduction: Since the beginning of the economic opening processes in the 1990s, investment flows have increased (FDI) worldwide. However, not all countries are proposed as ideal destinations for recipients of FDI, it must have an attractive economic, political and social landscape.
 Objetive: This research has the objective of studying the influence that the political risk may have on the decision-making on the subject of FDI by entrepreneurs, in particular, Colombians
 Methodology: The areas from where it has been analyzed, a series of low criteria is proposed. Is considered. It has been analyzed, a scale of value has been generated for each one, through those that have been studied. Means of stochastic multicriteria acceptability analysis.
 Results: The feasible weight space results point at the United States as the best destination for Colombian investment, followed by Brazil, the United Kingdom and Chile; while Panama, Spain and Mexico are not favored by any weighting.
 Conclusions: This work might be helpful in decision-making processes intended to reduce the uncertainty that is proper of the external environment.

Consensus-based failure mode and effect analysis in group decision-making with incomplete weights of risk factors: Case study of stereotactic body radiation therapy for lung cancer

Failure mode and effect analysis (FMEA) is a widely used management technique to identify potential failure modes in products, processes, systems, and services to assign limited resources for implementing improvement efforts. For the FMEA with a number of experts, the experts may take different influences on the decision-making process due to the difference between individual rationality and cognition and the influence of social relations. Besides, incomplete weights of risk factors are vital to capturing the fuzziness of experts’ evaluation. Therefore, this paper proposes a consensus-based FMEA method to explore that how cooperative relationship network of experts, the consensus process, and incomplete weight information of risk factors in FMEA influence the decision-making process. First, a consensus reaching process considering cooperative relationships between experts, the self-confidence of experts, and minimum adjustment of expert opinion is proposed to derive a collective evaluation of group. Afterward, the stochastic multicriteria acceptability analysis method is integrated with the gained and lost dominance score method to deal with incomplete weights of risk factors in the FMEA. The proposed method is employed in a case study about ranking the failure modes of stereotactic body radiation therapy for lung cancer patients. The robustness and feasibility of the proposed method are validated by comparative analysis.

A group decision making method with preference analysis to re-build the Global Entrepreneurship Index.

This study proposes a group decision making (GDM) method with preference analysis to re-build the Global Entrepreneurship Index (GEI). Specifically, a single decision maker is firstly identified using a specified individual judgement about the importance order of three sub-indices of the GEI. A preliminary group decision matrix is constructed in terms of taking all possible individual judgments into account. Then the analysis of the preferential differences and preferential priorities with respect to the preliminary group decision matrix is conducted to obtain a revised group decision matrix, in which preferential differences calculate the weighted differences as the degrees of differences among different alternatives for each decision maker, preferential priorities describe the favorite ranking of alternatives for each decision maker. Finally, we employ the Stochastic Multicriteria Acceptability Analysis for group decision-making (SMAA-2) to create the holistic acceptability indices for measuring the entrepreneurship performance. In addition, a satisfaction index is developed to indicate the merits of proposed GDM method. A case study using the GEI-2019 of 19 G20 countries is carried out to validate our GDM method.

Efficiency evaluation for decision making units with fixed-sum outputs using data envelopment analysis and stochastic multicriteria acceptability analysis

The generalized equilibrium efficient frontier data envelopment analysis (GEEFDEA) approach, an extension of the DEA method, has been widely used to solve the problem of evaluating decision making units (DMUs) producing fixed-sum outputs. It constructs a common equilibrium efficient frontier through a minimum reduction strategy for fixed-sum outputs and uses this frontier as a benchmark to achieve a complete ranking of DMUs. However, the existence of multiple feasible equilibrium efficient frontiers may lead to inconsistency in the evaluation criteria, and this possibility limits the method’s usefulness. In this paper, an integrated framework for solving this problem is proposed to rank DMUs by using stochastic multicriteria acceptability analysis (SMAA-2) method combined with the GEEFDEA approach. Instead of using a certain common equilibrium efficient frontier as in conventional GEEFDEA approaches, we explore all possible frontiers to answer various robustness questions by computing rank acceptability indices and pairwise winning indices. Furthermore, we derive the complete ranking from the dominance relationships among the DMUs. Two numerical examples are used to demonstrate the effectiveness and rationality of the proposed hybrid approach.