Ranking Alternatives on the Basis of a Dominance Intensity Measure

The additive multi-attribute utility model is widely used within MultiAttribute Utility Theory (MAUT), demanding all the information describing the decision-making situation. However, these information requirements can obviously be far too strict in many practical situations. Consequently, incomplete information about input parameters has been incorporated into the decisionmaking process. We propose an approach based on a dominance intensity measure to deal with such situations. The approach is based on the dominance values between pairs of alternatives that can be computed by linear programming. These dominance values are transformed into dominance intensities from which a dominance intensity measure is derived. It is used to analyze the robustness of a ranking of technologies for the disposition of surplus weapons-grade plutonium by the Department of Energy in the USA, and compared with other dominance measuring methods

Ranking Alternatives on the Basis of the Intensity of Dominance and Fuzzy Logic within MAUT

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 dominance measuring methods and other methodologies by Monte Carlo simulation techniques. The performance is analyzed in terms of two measures of efficacy: hit ratio, the proportion of all cases in which the method selects the same best alternative as in the TRUE ranking, and the Rank-order correlation, which represents how similar the overall rank structures of alternatives are in the TRUE ranking and in the ranking derived from the method. The approaches are illustrated with an example consisting on the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides

Dominance Measuring Approach using Stochastic Weights

In this paper we propose an approach to obtain a ranking of alternatives in multicriteria decision-making problems when there is imprecision concerning the alternative performances, component utility functions and weights. We assume decision maker's preferences are represented by an additive multi-attribute utility function, in which weights are modeled by independent normal variables, the performance in each attribute for each alternative is an interval value and classes of utility functions are available for each attribute. The approach we propose is based on dominance measures, which are computed in a similar way that when the imprecision concerning weights is modeled by uniform distributions or by an ordinal relation. In this paper we will show how the approach can be applied when the imprecision concerning weights are represented by normal distributions. Extensions to other distributions, such as truncated normal or beta, can be feasible using Monte Carlo simulation techniques

Dominance intensity measure within fuzzy weight oriented MAUT: an application

We introduce a dominance intensity measuring method 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) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers’ preferences, and imprecise weights are represented by trapezoidal fuzzy weights.The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights. An example concerning the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides illustrates the approach. Monte Carlo simulation techniques have been used to show that the proposed method performs well for different imprecision levels in terms of a hit ratio and a rank-order correlation measure

Dominance measuring methods within MAVT/MAUT with imprecise information concerning decision-makers'preferences

Dominance measuring methods are an approach for dealing with complex decision-making problems with imprecise information within multi-attribute value/utility theory. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in different ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we review dominance measuring methods proposed in the literature for dealing with imprecise information (intervals, ordinal information or fuzzy numbers) about decision-makers? preferences and their performance in comparison with other existing approaches, like SMAA and SMAA-II or Sarabando and Dias? method

Dominance Measuring Method Performance under Incomplete Information about Weights.

In multi-attribute utility theory, it is often not easy to elicit precise values for the scaling weights representing the relative importance of criteria. A very widespread approach is to gather incomplete information. A recent approach for dealing with such situations is to use information about each alternative?s intensity of dominance, known as dominance measuring methods. Different dominancemeasuring methods have been proposed, and simulation studies have been carried out to compare these methods with each other and with other approaches but only when ordinal information about weights is available. In this paper, we useMonte Carlo simulation techniques to analyse the performance of and adapt such methods to deal with weight intervals, weights fitting independent normal probability distributions orweights represented by fuzzy numbers.Moreover, dominance measuringmethod performance is also compared with a widely used methodology dealing with incomplete information on weights, the stochastic multicriteria acceptability analysis (SMAA). SMAA is based on exploring the weight space to describe the evaluations that would make each alternative the preferred one

Elaborations on Multiattribute Utility Theory Dominance

ELABORATIONS ON MULTIATTRIBUTE UTILITY THEORY DOMINANCE By David L. Vairo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. Virginia Commonwealth University, 2019. Major Director: Dissertation director’s name, Dr. Jason Merrick, Supply Chain Management and Analytics Multiattribute Utility Theory (MAUT) is used to structure decisions with more than one factor (attribute) in play. These decisions become complex when the attributes are dependent on one another. Where linear modeling is concerned with how factors are directly related or correlated with each other, MAUT is concerned with how a decision maker feels about the attributes. This means that direct elicitation of value or utility functions is required. This dissertation focuses on expanding the types of dominance forms used within MAUT. These forms reduce the direct elicitation needed to help structure decisions. Out of this work comes support for current criticisms of gain/loss separability that is assumed as part of Prospect Theory. As such, an alternative to Prospect Theory is presented, derived from within MAUT, by modeling the probability an event occurs as an attribute

Dominance measuring methods for the selection of cleaning services in a European underground transportation company

Dominance measuring methods are a recent approach for dealing with complex decisionmaking problems with imprecise, incomplete or partial information within multi-attribute value/utility theory. These methods compute pairwise dominance values and exploit the information included in the dominance matrix in different ways to derive measures of dominance intensity to rank the alternatives under consideration. We review dominance measuring methods proposed in the literature, describing how their possible drawbacks have been progressively overcome, and comparing their performance with other existing approaches, like surrogate weighting methods, the adaptation of classical decision rules to encompass an imprecise decision context, SMAA or Sarabando and Dias’ method. An example of the selection of cleaning services in a European underground transportation company is used to illustrate dominance measuring methods in a real complex decision-making problem

An information theory for preferences

Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative of a normalized utility function. A utility density function is non-negative and integrates to unity. These two properties form the basis of a correspondence between utility and probability. A natural application of this analogy is a maximum entropy principle to assign maximum entropy utility values. Maximum entropy utility interprets many of the common utility functions based on the preference information needed for their assignment, and helps assign utility values based on partial preference information. This paper reviews maximum entropy utility and introduces further results that stem from the duality between probability and utility

Cumulative dominance and heuristic performance in binary multi-attribute choice

Working paper 895, Department of Economics and Business, Universitat Pompeu FabraSeveral studies have reported high performance of simple decision heuristics in multi-attribute decision making. In this paper, we focus on situations where attributes are binary and analyze the performance of Deterministic-Elimination-By-Aspects (DEBA) and similar decision heuristics. We consider non-increasing weights and two probabilistic models for the attribute values: one where attribute values are independent Bernoulli randomvariables; the other one where they are binary random variables with inter-attribute positive correlations. Using these models, we show that good performance of DEBA is explained by the presence of cumulative as opposed to simple dominance. We therefore introduce the concepts of cumulative dominance compliance and fully cumulative dominance compliance and show that DEBA satisfies those properties. We derive a lower bound with which cumulative dominance compliant heuristics will choose a best alternative and show that, even with many attributes, this is not small. We also derive an upper bound for the expected loss of fully cumulative compliance heuristics and show that this is moderate even when the number of attributes is large. Both bounds are independent of the values of the weights.Postprint (author’s final draft