Modelling inaccurate determination, uncertainty, imprecision using multiple criteria

The purpose of this paper is to study how the consideration of several criteria, as opposed to a more traditional mono-criterion approach, helps the modelling of imprecision, uncertainty and inaccurate determination (I.U.I.D.) in a decision-aid study. After a brief review of the main sources of inaccurate determination, uncertainty and imprecision that arises in a decision-aid situation, we show that the use of multiple criteria allows to build partial preference structures, to discuss in a powerful way the precision of the evaluation on each criteria and to create a clear language between the actors via the use of the evaluation tableau. We argue that this proves useful in dealing with I.U.I.D. 1 Introduction. The use of multiple criteria in decision-aid models is often justified (see e.g. Zeleny (1982) or Sch rlig (1985)) by the fact that the world is governed by multiple objectives and that any decision implies to balance "pros" and "cons". This widely-shared point of view can however be criticized (see Bouyssou (1987) and Roy (1988b)). Using a mono-criterion approach to decision-aid does not imply that one considers that "reality" is governed by a single criterion. It is well-known that, in this kind of models, multiple objectives are often taken into account e.g. via the use of constraints, sensivity analysis and "prices" allowing to convert heterogeneous consequences into a single unit. As emphasized by Roy (1988b), the use of multiple criteria does not simply appear as a generalization of traditionnal approaches but constitutes a new paradigm for analysing and helping decisions. In this paper we wish to outline what we consider as an important justification for entering this new paradigm : the management of imprecision, uncertainty and inaccurate determination (I.U.I.D) that is part of most decision situations. Our analysis follows that of Roy (1988a). He distinguished four main sources of I.U.I.D. that the analyst has to deal with. We briefly present them in section 2. In section 3, we recall the main originalities of models explicitely using several criteria. In section 4 we try to show how the consideration of several criteria helps the modelling of I.U.I.D. and leads to models that are significantly different from those deriving from the consideration of a unique criterion in this respect. 2 The four main sources of uncertainty, imprecision and inaccurate determination in decision models (Roy (1988a)). a) The "map" is not the "territory". Locating a plant, chosing an equipment, investing in new activities are crucial decisions for a firm. The purpose of decision-aid is to compare such complex alternatives. If one wants to use a formal model of decision-aid, the complexity of these alternatives and their consequences makes it often impossible to compare them directly. This comparison is made possible through the use of "maps" of these complex "territories". For an alternative, a map consists of a model of the consequences of its implementation (in order to describe an alternative it is possible to use several maps of different "scale" using e.g. a hierarchical model). These maps create a tractable language that allows an effective communication between the various actors of the decision process and provides an adequate basis for the comparison of the alternatives. However the establishment of the maps inevitably involves many simplifications, omissions and distorsions which introduce in the model an important source of arbitrariness. Indeed, there are often several and equally valid ways of building these maps. While forced to use maps in order to compare territories, the analyst has to make a tradeoff between the richness and the readability of the maps : the "richer" is one map the closer it is to the territory, but the more difficult it may be to compare it to other maps. b) The "future" is not a "present" to come. The alternatives that are to be compared will only be implemented in a more or less distant future. Thus, at the time of the study, the consequences of the implementation of an alternative are very often unpredictable for they depend on environmental factors and/or the strategy of other actors that are still unknown and may well be influenced by the implementation of that alternative. This is the most classical source of I.U.I.D. that is mentionned in every textbook on decision models. Many efforts have been devoted to cope with this unpredictability using, e.g., probability distributions, plausibility measures, scenarios, etc. As Roy (1988a) mentionned, the unpredictability of the consequences of implementing an alternative also stems from the fact that the alternatives are not completely specified at the time of the study. When a firm tries to compare several sites for locating a new plant, the precise characteristics of each site may not have been completely investigated yet. Furthermore, the precise draft of the plant to be built may not be available and may well depend on the site chosen. Thus, even if one could predict with a very high precision the consequences of an alternative, an element of inaccurate determination would remain since the alternatives are still "projects". c) The data are not the result of exact measurement. The establishment of a map usually involves the consideration of two types of data. Data of type I are closely linked to the territory that the analyst wishes to describe. The modelling of uncertainty mentionned in the above paragraph will apply to this first type of data. For instance, suppose that an analyst has to evaluate the human consequences of building a polluting plant on a given site. He will have to cope with uncertainty since he will be forced to envisage various scenarios for the growth of the population in that area. He will also have to deal with imprecision since the present number of people living close to the projected plant is far from being perfectly known : counting houses on a map or on-site studies do not lead to precise evaluations. Thus, it is important to realize that many figures used in decision-aid models are only "order of magnitudes". This imprecision is often seen as stemming from the measurement techniques that are used. It also comes from the fact that, in many situations, the very definition of what "should" be measured is very imprecise. Using the same example as above, it is not clear how the analyst should take into account schools, hospitals, second homes, etc. This inaccurate determination of what is to be measured is certainly at least as important as the imprecision inherent to any kind of measurement. Data of type II concern the way the first type of data is used in the construction of the map. Parameters like discounting rates or utility functions designed to capture an attitude toward risk are examples of this second type of data. They are more linked to a particular value system than to an alternative. In our siting example such data could consist of the weight assigned to each inhabitant that is function of the distance between his residence and the projected plant, the attitude toward risk of the firm concerning the amount of nuisance created for the riparians, etc. Though techniques have been created to assess these data, it is important to keep in mind that they are very often "created" as well as "measured" (see e.g. the work of McCord and de Neufville (1983) concerning utility functions). d) The model is not the description of a real entity independent of the model. Data of the second type are connected with certain aspects of the preference system(s) of the actor(s) involved in the decision process. It is well known that the questionning process used by the analyst in order to obtain these data may significantly influence the answers (see Bouyssou (1984)). This is all the more true since the preference system of an actor may not be completely structured at the time of the study : areas of firm conviction may well coexist with areas of hesitation and ambiguity in which the influence of the model on what is to be "captured" is overwhelming. Furthermore, the various actors may well disagree and, as a result of a discussion, some actors may change their mind on some point thus creating some "inconsistencies" with previously stated judgements. In such cases the management of these hesitations, contradictions and conflicts seems a prerequisite to any convincing decision-aid model. This is linked to what Roy and Bouyssou (1986) called a constructive attitude towards decision-aid, as opposed to a descriptive one, in which the role of the analyst is not to describe as accurately as possible supposedly pre-existing preferences but to provide information and tools that are useful for justifying, building and arguing preferences. 3 The multiple criteria approach to decision-aid. From the point of view of the management of I.U.I.D., the main feature of an approach using multiple criteria is to break down the modelling process into two different phases : the construction of the criteria (which gives rise to the evaluation tableau) and the aggregation of these criteria (see Fig. 1). As advocated by Roy (1985), the analyst should use the smallest possible amount of type II data in the construction of the various criteria. We noted in section 2, that some data of type II such as utility functions have to be taken into account in order to build the criteria. However, sensitive information such as the tradeoffs between the various criteria are only introduced in the aggregation phase, contrary to what is usually done in a mono-criterion approach in which the construction of the unique criterion involves at the same time data of both types. This approach is based on what could be called an "act of faith", i.e., the belief that the explicit construction of several criteria will have a "positive role" in the modelling process. It rests on an underlying assumption stating that in most decision-aid studies it is possible to identify a small number of "points of view" (usually between three and no more than ten, at least at the upper level if a hierarchical model is used) around which it is possible to build a familly of criteria that is exhaustive and simple enough to be accepted as a basis of discussion by all the actors of the decision process. ________________________________________________________________ _ ______________________ _ _ _ Set of Alternatives_ _ _ ______________________ _ _ ___________________________________________ _ _ _ _____________ _______________________ _ _ _________Type I data______ Evaluation Tableau __ _ _ _ _____________ _ _g1 g2 ... gn __ _ _ _ _ _ _ _ ___ ________________ __ _______________________ ______________ _ a1_ __ __ Unique Criterion ___Type II data_ _ a2_ __ _______________________ ______________ _ : _ __ _ _ _ _______________________ _ _ _ ______________________ _ _ _ _Aggregation techni-__ _ _ ____________ques/Interactive __