Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis in multiple criteria hierarchy process for the Choquet integral preference model

The paper deals with two important issues of Multiple Criteria Decision Aiding: interaction between criteria and hierarchical structure of criteria. To handle interactions, we apply the Choquet integral as a preference model, and to handle the hierarchy of criteria, we apply the recently proposed methodology called Multiple Criteria Hierarchy Process. In addition to dealing with the above issues, we suppose that the preference information provided by the Decision Maker is indirect and has the form of pairwise comparisons of criteria with respect to their importance and pairwise preference comparisons of some pairs of alternatives with respect to some criteria. In consequence, many instances of the Choquet integral are usually compatible with this preference information. These instances are identified and exploited by Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis. To illustrate the whole approach, we show its application to a real world decision problem concerning the ranking of universities for a hypothetical Decision Maker.     

An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule

The ELECTRE (ELimination Et Choix Traduisant la REalité, in French) is an effective multiple criteria decision making method based on comparative analysis. Among the family of the ELECTRE methods and their extensions, the ELECTRE III is widely used since it can tackle uncertain and imprecise information. The hesitant fuzzy linguistic term set can represent people's perceptions more comprehensively and flexibly than exact numbers especially in cognitive complex decision-making process. In this paper, we develop an integrated method based on the ELECTRE III to handle the cognitive complex multiple experts multiple criteria decision making problems in which the cognitive complex information is represented by hesitant fuzzy linguistic term sets and the outranking relations between alternatives are calculated by a novel score-function-based distance measure between hesitant fuzzy linguistic elements. A combinative weight-determining method involving both subjective and objective opinions of experts is introduced to derive the weights of criteria. After obtaining the ranking of alternatives from each experts’ decision matrix by the distillation algorithm, the weighted Borda rule is implemented to aggregate the rankings of alternatives regarding different experts. Some ordinal consensus measures are introduced to identify the reliability of the final ranking result. An application of hospital ranking in China is provided to validate the efficiency of the proposed method.     

Evaluation of Multicriteria Decision Analysis Algorithms in Food Safety: A Case Study on Emerging Zoonoses Prioritization

Decision making in food safety is a complex process that involves several criteria of different nature like the expected reduction in the number of illnesses, the potential economic or health-related cost, or even the environmental impact of a given policy or intervention. Several multicriteria decision analysis (MCDA) algorithms are currently used, mostly individually, in food safety to rank different options in a multifactorial environment. However, the selection of the MCDA algorithm is a decision problem on its own because different methods calculate different rankings. The aim of this study was to compare the impact of different uncertainty sources on the rankings of MCDA problems in the context of food safety. For that purpose, a previously published data set on emerging zoonoses in the Netherlands was used to compare different MCDA algorithms: MMOORA, TOPSIS, VIKOR, WASPAS, and ELECTRE III. The rankings were calculated with and without considering uncertainty (using fuzzy sets), to assess the importance of this factor. The rankings obtained differed between algorithms, emphasizing that the selection of the MCDA method had a relevant impact in the rankings. Furthermore, considering uncertainty in the ranking had a high influence on the results. Both factors were more relevant than the weights associated with each criterion in this case study. A hierarchical clustering method was suggested to aggregate results obtained by the different algorithms. This complementary step seems to be a promising way to decrease extreme difference among algorithms and could provide a strong added value in the decision-making process.     

Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE

Robust Ordinal Regression (ROR) supports Multiple Criteria Decision Process by considering all sets of parameters of an assumed preference model, that are compatible with preference information elicited by a Decision Maker (DM). As a result of ROR, one gets necessary and possible preference relations in the set of alternatives, which hold for all compatible sets of parameters, or for at least one compatible set of parameters, respectively. In this paper, we propose an extension of ELECTRE and PROMETHEE methods to the case of the hierarchy of criteria, which was never considered before. Then, we adapt ROR to the hierarchical versions of ELECTRE and PROMETHEE methods.     

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as “outranking relations” to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.     

Ranking irregularities when evaluating alternatives by using some ELECTRE methods

The ELECTRE II and III methods enjoy a wide acceptance in solving multi-criteria decision-making (MCDM) problems. Research results in this paper reveal that there are some compelling reasons to doubt the correctness of the proposed rankings when the ELECTRE II and III methods are used. In a typical test we first used these methods to determine the best alternative for a given MCDM problem. Next, we randomly replaced a non-optimal alternative by a worse one and repeated the calculations without changing any of the other data. Our computational tests revealed that sometimes the ELECTRE II and III methods might change the indication of the best alternative. We treat such phenomena as rank reversals. Although such ranking irregularities are well known for the additive variants of the AHP method, it is the very first time that they are reported to occur when the ELECTRE methods are used. These two methods are also evaluated in terms of two other ranking tests and they failed them as well. Two real-life cases are described to demonstrate the occurrence of rank reversals with the ELECTRE II and III methods. Based on the three test criteria presented in this paper, some computational experiments on randomly generated decision problems were executed to test the performance of the ELECTRE II and III methods and an examination of some real-life case studies are also discussed. The results of these examinations show that the rates of the three types of ranking irregularities were rather significant in both the simulated decision problems and the real-life cases studied in this paper.     

Beyond Markowitz with multiple criteria decision aiding

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.     

Consumer preference analysis: A data-driven multiple criteria approach integrating online information

Multiple criteria approaches can assist the product manager to know the consumer preferences in the context of e-commerce. Consumer preference analysis explains what aspects of a product affect and how they affect a consumer’s purchasing decision. This issue plays an important role in e-commerce platforms from its relevance in marketing decisions such as advertisements, recommendations and promotions. In this regard, we propose a data-driven multiple criteria decision aiding (MCDA) approach to integrate online information, such as explicit (e.g., reviews and ratings) and implicit (e.g., clicks and purchases) feedback from consumers. However, MCDA approaches present a critical challenge that even an experienced product manager could find it difficult to pre-define the criteria on which a product is evaluated. To address this issue, our proposed approach first utilizes text-mining techniques to assist the product manager identify the criteria, and then determines and collects the relative importance of the criteria and their values. Given the criteria information, we use a sampling process to provide two indices, the consumer preference index and rank acceptability index. The first index helps in prioritizing the pairwise comparisons of products, while the second one helps in deriving a default ranking list for first-time-registered consumers. We record the products viewed by consumers and generate their preference information in the form of pairwise comparisons for analyses within an aggregation-disaggregation paradigm. We also provide a representative value function to help the product manager gain insight into the preferences. Finally, we describe how a real-world application including the product manager and consumers exploits the proposed approach on an e-commerce platform to take a large step toward aiding more realistic and data-driven multiple criteria decision making.     

A Sensitivity Analysis Approach for Some Deterministic Multi-Criteria Decision-Making Methods*

Often, data in multi-criteria decision making (MCDM) problems are imprecise and changeable. Therefore, an important step in many applications of MCDM is to perform a sensitivity analysis on the input data. This paper presents a methodology for performing a sensitivity analysis on the weights on the decision criteria and the performance values of the alternatives expressed in terms of the decision criteria. The proposed methodology is demonstrated on three widely used decision methods. These methods are the weighted sum model (WSM), the weighted product model (WPM), and the analytic hierarchy process (AHP). This paper formalizes a number of important issues on sensitivity analysis and derives some critical theoretical results. Also, a number of illustrative examples and computational experiments further illustrate the application of the proposed methodology.     

Extreme ranking analysis in robust ordinal regression

We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTA^GMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEE^GKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.     

An analytic hierarchy process based simulation model for entry mode decision regarding foreign direct investment

A methodology is developed for ranking entry mode alternatives encountered by individual firms considering foreign direct investment (FDI). The methodology deals with the risks and uncertainties related to FDI. The analytic hierarchy process (AHP) is used to solve the multiple criteria decision-making problem using input from a firm's management. A simulation approach is incorporated into the AHP to handle the uncertainty considerations encountered in an FDI environment. The uncertainties include: (1) uncertainty regarding the future characteristics of the FDI decision making environment, (2) uncertainty associated with the decision maker's judgment regarding pairwise comparisons necessitated by the AHP.     

A Multifactorial Risk Prioritization Framework for Foodborne Pathogens

We develop a prioritization framework for foodborne risks that considers public health impact as well as three other factors (market impact, consumer risk acceptance and perception, and social sensitivity). Canadian case studies are presented for six pathogen‐food combinations: Campylobacter spp. in chicken; Salmonella spp. in chicken and spinach; Escherichia coli O157 in spinach and beef; and Listeria monocytogenes in ready‐to‐eat meats. Public health impact is measured by disability‐adjusted life years and the cost of illness. Market impact is quantified by the economic importance of the domestic market. Likert‐type scales are used to capture consumer perception and acceptance of risk and social sensitivity to impacts on vulnerable consumer groups and industries. Risk ranking is facilitated through the development of a knowledge database presented in the format of info cards and the use of multicriteria decision analysis (MCDA) to aggregate the four factors. Three scenarios representing different stakeholders illustrate the use of MCDA to arrive at rankings of pathogen‐food combinations that reflect different criteria weights. The framework provides a flexible instrument to support policymakers in complex risk prioritization decision making when different stakeholder groups are involved and when multiple pathogen‐food combinations are compared.     

How to support the application of multiple criteria decision analysis? Let us start with a comprehensive taxonomy

Decision making is a complex task that involves a multitude of perspectives, constraints, and variables. Multiple Criteria Decision Analysis (MCDA) is a process that has been used for several decades to support decision making. It includes a series of steps that systematically help Decision Maker(s) (DM(s)) and stakeholders in structuring a decision making problem, identifying their preferences, and building a decision recommendation consistent with those preferences. Over the last decades, many studies have demonstrated the conduct of the MCDA process and how to select an MCDA method. Until now, there has not been a review of these studies, nor a proposal of a unified and comprehensive high-level representation of the MCDA process characteristics (i.e., features), which is the goal of this paper. We introduce a review of the research that defines how to conduct the MCDA process, compares MCDA methods, and presents Decision Support Systems (DSSs) to recommend a relevant MCDA method or a subset of methods. We then synthesize this research into a taxonomy of characteristics of the MCDA process, grouped into three main phases, (i) problem formulation, (ii) construction of the decision recommendation, and (iii) qualitative features and technical support. Each of these phases includes a subset of the 10 characteristics that helps the analyst implementing the MCDA process, while also being aware of the implication of these choices at each step. By showing how decision making can be split into manageable and justifiable steps, we reduce the risk of overwhelming the analyst, as well as the DMs/stakeholders during the MCDA process. A questioning strategy is also proposed to demonstrate how to apply the taxonomy to map MCDA methods and select the most relevant one(s) using real case studies. Additionally, we show how the DSSs for MCDA method recommendation can be grouped into three main clusters. This proposal can enhance a traceable and categorizable development of such systems.     

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

This paper presents a methodology for analyzing Analytic Hierarchy Process (AHP) rankings if the pairwise preference judgments are uncertain (stochastic). If the relative preference statements are represented by judgment intervals, rather than single values, then the rankings resulting from a traditional (deterministic) AHP analysis based on single judgment values may be reversed, and therefore incorrect. In the presence of stochastic judgments, the traditional AHP rankings may be stable or unstable, depending on the nature of the uncertainty. We develop multivariate statistical techniques to obtain both point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. If the rank reversal probability is low, then the rankings are stable and the decision maker can be confident that the AHP ranking is correct. However, if the likelihood of rank reversal is high, then the decision maker should interpret the AHP rankings cautiously, as there is a subtantial probability that these rankings are incorrect. High rank reversal probabilities indicate a need for exploring alternative problem formulations and methods of analysis. The information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision-making process, much like variability and confidence intervals are crucial tools for statistical inference. We provide simulation experiments and numerical examples to evaluate our method. Our analysis of rank reversal due to stochastic judgments is not related to previous research on rank reversal that focuses on mathematical properties inherent to the AHP methodology, for instance, the occurrence of rank reversal if a new alternative is added or an existing one is deleted.     

A multi-criteria ranking algorithm (MCRA) for determining breast cancer therapy

Breast cancer is the leading cause of cancer deaths among women. The selection of an effective, patient-specific treatment plan for breast cancer has been a challenge for physicians because the decision process involves a vast number of treatment alternatives as well as treatment decision criteria, such as the stage of the cancer (e.g., in situ, invasive, metastasis), tumor characteristics, biomarker-related risks, and patient-related risks. Furthermore, every patient's case is unique, requiring a patient-specific treatment plan, while there is no standard procedure even for a particular stage of the breast cancer. In this paper, we first determine a comprehensive set of criteria for selecting the best breast cancer therapy by interviewing medical oncologists and reviewing the literature. We then present two analytical hierarchy process (AHP) models for quantifying the weights of criteria for breast cancer treatment in two sequential steps: primary and secondary treatment therapy. Using the weights of criteria from the AHP model, we propose a new multi-criteria ranking algorithm (MCRA), which evaluates a large variety of patient scenarios and provides the best patient-tailored breast cancer treatment alternatives based on the input of nine medical oncologists. We then validate the predictions of the multi-criteria ranking algorithm by comparing treatment ranks of the algorithm with ranks of five different oncologists, and show that algorithm rankings match or are statistically significantly correlated with the overall expert ranking in most cases. Our multi-criteria ranking algorithm could be used as an accessible decision-support tool to aid oncologists and educate patients for determining appropriate and effective treatment alternatives for breast cancer. Our approach is also general in the sense that it could be adapted to solve other complex decision-making problems in medicine, healthcare, as well as other service and manufacturing industries.     

Market segmentation: A multiple criteria approach combining preference analysis and segmentation decision

We propose a new multiple criteria decision aiding approach for market segmentation that integrates preference analysis and segmentation decision within a unified framework. The approach employs an additive value function as the preference model and requires consumers to provide pairwise comparisons of some products as the preference information. To analyze each consumer’s preferences, the approach applies the disaggregation paradigm and the stochastic multicriteria acceptability analysis to derive a set of value functions according to the preference information provided by each consumer. Then, each consumer’s preferences can be represented by the distribution of possible rankings of products and associated support degrees by applying the derived value functions. On the basis of preference analysis, a new metric is proposed to measure the similarity between preferences of different consumers, and a hierarchical clustering algorithm is developed to perform market segmentation. To help firms serve consumers from different segments with targeted marketing policies and appropriate products, the approach proposes to work out a representative value function and the univocal ranking of products for each consumer so that products that rank in the front of the list can be presented to her/him. Finally, an illustrative example of a market segmentation problem details the application of the proposed approach.     

Interval-based extensions of two outranking methods for multi-criteria ordinal classification

We present two new interval-based extensions of ELECTRE TRI-nB and ELECTRE TRI-nC, in which the preference relations are built by using the interval outranking approach. The boundaries between adjacent classes (or categories) are described by a set of limiting profiles, whose criteria could take on values which are interval numbers. Compared to INTERCLASS (a recently proposed interval-based ordinal classification method), the assignments suggested by our first extension come from enhanced preference relations between the actions and limiting boundaries and are likely to be more appropriate. In addition, it can suggest assignments from a pseudo-conjunctive logic. In our second extension, each class is characterized by a set of representative actions, again allowing interval numbers as criterion scores. The outranking relations between actions and classes are enhanced by having several representative actions in each category. Both new extensions can handle imperfect knowledge of the model parameters (weights, veto thresholds, credibility threshold), even missing criterion scores. Some fundamental properties and results are proved to guarantee the consistency of the methods, which are also illustrated with some numerical examples.     

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.     

Heuristics for prioritizing pair-wise elicitation questions with additive multi-attribute value models

Additive value models are widely used in Multiple Criteria Decision Analysis. Direct elicitation of the value model preference parameters can impose excessive cognitive burden on the decision maker. Indirect techniques that employ pair-wise questions have been proposed for lowering the elicitation effort. In all practically relevant problems, more than a single question needs to be answered for arriving at a sufficiently precise outcome. The selection and ordering of questions affects the number of answers required for ranking the decision alternatives. However, evaluating all possible questions and answers is intractable due to the search space being, in the worst case, of factorial size. This paper develops heuristics for prioritizing pair-wise elicitation questions based on (1) necessary preference relations, (2) extreme ranks attained by the alternatives, (3) pair-wise preference indices, and (4) rank acceptability indices. We also introduce three metrics for assessing quality of a question prioritization heuristic. Numerical results allow us to identify a subset of heuristics that score well on our metrics in a variety of problem settings. This conclusion was validated in a real-world experiment where 101 subjects answered pair-wise questions to rank 10 mobile phone packages evaluated in terms of four criteria.     

Uses and Misuses of Multicriteria Decision Analysis (MCDA) in Environmental Decision Making

We focus on a class of multicriteria methods that are commonly used in environmental decision making—those that employ the weighted linear average algorithm (and this includes the popular analytic hierarchy process (AHP)). While we do not doubt the potential benefits of using formal decision methods of this type, we draw attention to the consequences of not using them well. In particular, we highlight a property of these methods that should not be overlooked when they are applied in environmental and wider decision-making contexts: the final decision or ranking of options is dependent on the choice of performance scoring scales for the criteria when the criteria weights are held constant. We compare this "sensitivity" to a well-known criticism of the AHP, and we go on to describe the more general lesson when it comes to using weighted linear average methods—a lesson concerning the relationship between criteria weights and performance scoring scales.