ACUTA: A novel method for eliciting additive value functions on the basis of holistic preference statements (original) (raw)
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We present a new method, called UTA GMS , for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A R A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA GMS method is intended to be used interactively, with an increasing subset A R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA GMS software. Some extensions of the method are also presented.
Omega-International Journal of Management Science, 2013
In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.
Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions
European Journal of Operational Research, 2008
We present a new method, called UTA GMS , for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A R ⊆ A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA GMS method is intended to be used interactively, with an increasing subset A R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA GMS software. Some extensions of the method are also presented.
Decision Aiding Assessing non-additive utility for multicriteria decision aid
2004
In the framework of Multi-Attribute Utility Theory (MAUT) several methods have been proposed to build a Decision-MakerÕs (DM) utility function representing his/her preferences. Among such methods, the UTA method infers an additive utility function from a set of exemplary decisions using linear programming. However, the UTA method does not guarantee to find a utility function which is coherent with the available information. This drawback is due to the underlying utility model of UTA, viz. the additive one, which does not allow to include additional information such as an interaction among criteria. In this paper we present a methodology for building a non-additive utility function, in the framework of the so called fuzzy integrals, which permits to model preference structures with interaction between criteria. Like in the UTA method, we aim at searching a utility function representing the DMÕs preferences, but unlike UTA, the functional form is a specific fuzzy integral (Choquet integral). As a result, we obtain weights which can be interpreted as the ''importance'' of coalitions of criteria, exploiting the potential interaction between criteria, as already proposed by other authors. However, within the same framework, we obtain also the marginal utility functions relative to each one of the considered criteria, that are evaluated on a common scale, as a consequence of the implemented methodology. Finally, we illustrate our approach with an example.
Ranking Alternatives on the Basis of the Intensity of Dominance and Fuzzy Logic within MAUT
2010
We introduce dominance measuring methods to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision making problems on the basis of Multi-Attribute Utility Theory (MAUT). We consider the situation where the alternative performances are represented by uniformly distributed intervals, and there exists imprecision concerning the decision-makers? preferences, by means of classes of individual utility functions and imprecise weights represented by weight intervals or fuzzy weights, respectively. An additive multi-attribute utility model is used to evaluate the alternatives under consideration, which is considered a valid approach in most practical cases. The approaches we propose are based on the dominance values between pairs of alternatives that can be computed by linear programming, which are then transformed into dominance intensities from which a dominance intensity measure is derived. The methods proposed are compared with other existing domi...
European Journal of Operational Research, 2009
We present a method called GRIP (Generalized Regression with Intensities of Preference) for ranking a set of actions evaluated on multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions, called reference actions. It constructs not only the preference relation in the considered set of actions, but it also gives information about intensities of preference for pairs of actions from this set for a given Decision Maker (DM). Distinguishing necessary and possible consequences of prefernce information on the all set of actions, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of UTA method based on ordinal regression. GRIP can also be compared to AHP method, which requires pairwise comparison of all actions and criteria, and yields a priority ranking of actions. As for the preference information being used, GRIP can be compared, moreover, to MAC-BETH method which also takes into account a preference order of actions and intensity of preference for pairs of actions. The preference information used in GRIP does not need, however, to be complete: the DM is asked to provide comparisons of only those pairs of reference actions on particular criteria for which his/her judgment is sufficiently certain. This is an important advantage comparing to methods which, instead, require comparison of all possible pairs of evaluations on all the considered criteria. Moreover, GRIP works with a set of general additive value functions compatible with the preference information, while other methods use a single and less general value function, such as the weighted-sum.
Multiple criteria decision making: Discordant preferences and problem description
Journal of Systems Science and Systems Engineering, 2007
There are many practical decision problems where decision makers' preferences may be inconsistent and contradictory. In this paper, new methods for ordering and classifying multi-attribute objects by discordant collective preferences are suggested. These methods are based on the theory of multiset metric spaces. The proposed techniques are applied to ranking companies and a competitive selection of projects, which are estimated by several experts upon multiple qualitative criteria.
An approach for finding the most preferred alternative in the presence of multiple criteria
European Journal of Operational Research, 1992
An interactive approach for discrete multiple criteria decision making problems is developed. The approach requires the decision maker to compare pairs of presented alternatives. These alternatives may be existing alternatives or dummy alternatives created from existing alternatives. Inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses. The approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function. The aim is to keep the number of pairwise comparisons required of the decision maker as small as possible. Computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches.
Ranking methods for valued preference relations
European Journal of Operational Research, 1992
In this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation. This method which is used in the MCDM method PROMETHEE I, is based on "leaving" and "entering" flows. We show that this method is characterized by a system of three independent axioms. I-Introduction Suppose that a number of decision alternatives are to be compared taking into account different points of view, e.g. several criteria or the opinion of several voters. As argued in Barrett et al. (1990) and Bouyssou (1990), a common practice in such situations is to associate with each ordered pair (a, b) of alternatives, a number indicating the strength or the credibility of the proposition "a is at least as good as b", e.g. the sum of the weights of the criteria favoring a or the percentage of voters declaring that a is preferred or indifferent to b. In this paper we study a particular method allowing to build a partial ranking, i.e. a reflexive and transitive binary (crisp) relation 2 , on A given such information. Since a partial ranking is not necessarily complete, the method considered in this paper will allow two alternatives to be declared incomparable. Though this may seem strange, it must not be forgotten that the available information may be very poor or conflictual. Declaring that a and b are incomparable thus means that it seems difficult to take, at least at this stage of the study, a definite position on the comparison of a and b.