شبکه ی بیزی برای عود چند معیاره و مشکلات تصمیم گیری چند معیاری: انتخاب صندلی چرخدار دستی

This paper discusses recurrent multi-criteria, multi-attribute decision problems. Because of the possibility of decision-maker ignorance or low decision-maker involvement the decision problem structuring is done once for all by a group of experts and does not involve the implication of the decision makers. We propose an original model based on Bayesian networks, which provides a decision process that helps the decision-maker to select an appropriate alternative among a set of alternatives, taking into account multiple criteria that are often conflicting. Our model makes it possible to represent in the same model the decision case (i.e., the decision-maker characteristics, contextual characteristics, their needs and preferences), the set of alternatives with the different attributes, and the choice criteria. The model allows us to compute the value of three essential elements: the importance of each criterion, which is based on the decision-case characteristics; each criterion’s evaluation index in terms of the alternative; and each criterion’s satisfaction index. The recurrent problem of choosing a manual wheelchair (MWC) illustrates the construction and use of our model.

A wheelchair is a device designed to replace walking, thus constituting a technical aid for mobility. A manual wheelchair (MWC) is a mechanical device made of hundreds of pieces and includes generally dozens of settings and options. Medical professionals recommend using a MWC to very different people with a physical disability, prescribing for each of them a particular type of MWC and specifying the settings and options that will best suit to this person in terms of the needs and preferences identified. Choosing a MWC requires clinicians with expertise, both clinical experience and a good knowledge of MWC. Unfortunately, these clinicians are very few compared to the number of cases. For each new MWC choice, their presence – face-to-face or even face-to-screen, as proposed by Kim, Kim, and Schmeler (2012) – is not possible. Choosing a MWC also requires much information about the person who will use the wheelchair, his/her abilities, needs, preferences, environment and constraints. In practice, the expert visits the places where the wheelchair is used. Making available expertise, knowledge and information needed to select an appropriate MWC is essential to improve the current choice processes. This will reduce the inequalities due to the frequent absence of experts during the choosing process. Since making a poor choice often leads to reduce the mobility of the person (e.g., due to a great lack of maneuverability, or comfort of propulsion, crossing obstacles, transfers, personal care attendants, or loading MWC in the car), making better choice will increase the mobility of people with physical disabilities and reduce health expenses due to negative consequences of choosing an inappropriate. Choosing a MWC need means accessing information about advantages and disadvantages of any MWC. Wheelchair users need help and explanations to simplify what is important in a given case; wheelchair users need to understand why some MWC characteristics of the MWC are especially needed in some situations, and the risks that result if they not follow these characteristics. This article is one of the results of the research project SACR FRM1 in France (Lepoutre, 2011). About 50% of the MWC used in France are not well adapted to the person, which may lead to reduced autonomy, inconvenience, pain, bedsores, and musculoskeletal disorders. This project made it possible to collect and formalize knowledge in order to complete a knowledged-based system to support choosing and regulating a MWC. This domain’s expert knowledge concerns specific perspectives, such as propulsion biomechanics (Desroches et al., 2010, Koontz et al., 2007, Mulroy et al., 2004 and Yoshimasa et al., 2010), transfer biomechanics (Debril et al., 2009 and Gagnon et al., 2009), quality criteria and general or specific rules for choosing a MWC (Guillon et al., 2009 and Tomlinson, 2000) and a CERAH2 course. In addition, much has been learned from of the Garches Institute’s experts,3 who propose a specific service for choosing and regulating a MWC. The project allowed us to identify, homogenize and list the characteristics of people, their environment and their life projects that would be likely to influence the choice. The MWC characteristics and the criteria have also been listed. The current available information about MWC in France (Girault, Dias, & Fodé, 2011) allows the user to list the references of MWC responding to a short list of binary conditions over the MWC attributes. This assistance is not enough to give an authoritative recommendation. We explain the reasons for chosing a Bayesian network model to deal with this kind of recurrent decision problem. We chose a Bayesian network since this model is specialized in representing many sources of uncertainty and in propagating any observed variables on some others. Choosing a MCW is seen as a decision problem with uncertainty. The first level of uncertainty concerns the factors that influence the choice that may be uncertain: for example, the data can be incomplete or imprecise, as well as qualitative or quantitative. The second level of uncertainty concerns the way the different factors influence the choice: for example, the ability of the MWC user to stand affects the importance of the stability criterion, but this influence is not deterministic. The MWC evaluation in terms of a given criterion is also not deterministic, since most criteria are not measurable, except for the total cost. Choosing a MWC is a recurrent decision problem. For each decision case, the alternatives set and the reasoning are the same. The problem is to select a MWC alternative that is appropriate for the person concerned by the choice, each one makes his/her choice by taking into account his/her own specificities, constraints and priorities. Since a recurrent problem concerns a wide range of decision-makers, we consider the possibility of decision-maker ignorance or low decision-maker involvement. The decision is considered to be made by a single decision-maker, even though several people are involved in the choice process. In practice, it is often a general practitioner with a MWC retailer, who may be a pharmacist. In the best cases, the choice is made by a multi-disciplinary team, including a rehabilitation specialist, an occupational therapist or a physical therapist, or a social worker. The person who uses the MWC is the first to benefit or to put up with the MWC choice. The personal care attendants are also very concerned by the quality of the choice of the MWC. For example, they push the MWC, they help the person to stand up, or they carry the MWC and put it in the car. These problem characteristics motivate our choice to use probabilistic graphical models, such as Bayesian networks (Darwiche, 2009 and Jensen and Nielsen, 2007), since it brings expert knowledge to the decision-maker. The experts are highly solicited during the model’s construction phase in order to provide the list of variables (i.e., attributes of the alternatives, characteristics of the decision case, criteria), the relationships between these variables, and the conditional probability tables. The same model can then be used for each new decision case by non-expert users. Lacking a MWC expert, choosing an appropriate MWC becomes possible. For this reason, the decision-maker is sometimes referred to as the user of the decision support system. The rest of the paper is organized as follows. Section 2 presents some issues in relation to the problem. Section 3 proposes our model, including a brief presentation of Bayesian networks. Section 4 describes the operations of our decision process. Section 5 discusses about our model in terms of the related works. Section 6 offers our conclusions and presents our future research prospects.

In this paper, we proposed a Bayesian network model for recurrent decision problems, such as choosing a manual wheelchair (MWC). We explain how to build a unique BN that can be used for any decision case of a recurrent multi criteria decision problem. Our model provides help to any kind of users, whether or not they are aware of the decision problem, just by integrating the known decision-case characteristics in the model. This model provides a list of probabilistic recommendations for the attributes of the alternatives. These probabilistic recommendations are very helpful for choosing a small number of alternatives before the final selection. This recommendations list appears in an early step of the decision process. The model also provides two interesting results: the probabilistic evaluation of the importance of the criteria in terms of the decision case, and a probabilistic evaluation of the satisfaction provided by a selected alternative in terms of each criterion for a given decision case. Building the Bayesian network model requires a lot of expert knowledge to determine what variables are susceptible to influence the choice and how. These variables concern the personal characteristics and the decisional context, including the external factors that cannot be controlled. These variables can be related to the constraints and/or can help to evaluate the importance of the criteria and obtain the evaluation of a given alternative for a given criterion. The users can use the system without answering any questions about preferences, using the links from factors to the importance indices. The importance of the criteria is the role of the domain experts when building the model. However, the user is allowed to manually modify the level of importance of each criterion. Our model has the advantage of unlimited criteria, while the studies about multi criteria decision method recommend to limit the number of criteria due to the decision-maker reasoning capacity. When building the BN, very specific criteria can be added to the model without modifying the local models for other criteria. These local models of the different criteria can be defined by the different experts. In addition, even though the size of the BN increases with the number of criteria, this is not a problem in terms of inference thanks to cutting BN into two BNs. Many criteria is not a problem since the user do not have to be informed about the criteria with very low importance. This proposal has several future research perspectives. The first perspective concerns an ideal alternative recommendation rather than a list of attribute recommendations. However, for each attribute, selecting the value with the higher probability does not provide an ideal alternative. A heuristic could be proposed that defines an order for the attributes, selects the attribute value, and propagates this selection in the BN before selecting the value of the next attribute. Another perspective is to adapt our model to the problems with several decision-makers, with each decision-maker having his/her own perspective and preference.