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

The design of aircraft using the decision support problem technique

The Decision Support Problem Technique for unified design, manufacturing and maintenance is being developed at the Systems Design Laboratory at the University of Houston. This involves the development of a domain-independent method (and the associated software) that can be used to process domain-dependent information and thereby provide support for human judgment. In a computer assisted environment, this support is provided in the form of optimal solutions to Decision Support Problems

The Möbius transform on symmetric ordered structures and its application to capacities on finite sets

Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry necessarily entails non associativity, hence computing rules are defined in order to deal with non associativity. We study in details computing rules, which we endow with a partial order. This permits to find solutions to the inversion formula underlying the Möbius transform. Then we apply these results to the case of capacities, a notion from decision theory which corresponds, in the language of ordered sets, to order preserving mappings, preserving also top and bottom. In this case, the solution of the inversion formula is called the Möbius transform of the capacity. Properties and examples of Möbius transform of sup-preserving and inf-preserving capacities are given.

Robust Algorithms for the Secretary Problem

In classical secretary problems, a sequence of n elements arrive in a uniformly random order, and we want to choose a single item, or a set of size K. The random order model allows us to escape from the strong lower bounds for the adversarial order setting, and excellent algorithms are known in this setting. However, one worrying aspect of these results is that the algorithms overfit to the model: they are not very robust. Indeed, if a few "outlier" arrivals are adversarially placed in the arrival sequence, the algorithms perform poorly. E.g., Dynkin’s popular 1/e-secretary algorithm is sensitive to even a single adversarial arrival: if the adversary gives one large bid at the beginning of the stream, the algorithm does not select any element at all. We investigate a robust version of the secretary problem. In the Byzantine Secretary model, we have two kinds of elements: green (good) and red (rogue). The values of all elements are chosen by the adversary. The green elements arrive at times uniformly randomly drawn from [0,1]. The red elements, however, arrive at adversarially chosen times. Naturally, the algorithm does not see these colors: how well can it solve secretary problems? We show that selecting the highest value red set, or the single largest green element is not possible with even a small fraction of red items. However, on the positive side, we show that these are the only bad cases, by giving algorithms which get value comparable to the value of the optimal green set minus the largest green item. (This benchmark reminds us of regret minimization and digital auctions, where we subtract an additive term depending on the "scale" of the problem.) Specifically, we give an algorithm to pick K elements, which gets within (1-ε) factor of the above benchmark, as long as K ≥ poly(ε^{-1} log n). We extend this to the knapsack secretary problem, for large knapsack size K. For the single-item case, an analogous benchmark is the value of the second-largest green item. For value-maximization, we give a poly log^* n-competitive algorithm, using a multi-layered bucketing scheme that adaptively refines our estimates of second-max over time. For probability-maximization, we show the existence of a good randomized algorithm, using the minimax principle. We hope that this work will spur further research on robust algorithms for the secretary problem, and for other problems in sequential decision-making, where the existing algorithms are not robust and often tend to overfit to the model.ISSN:1868-896

QUALITATIVE ANSWERING SURVEYS AND SOFT COMPUTING

In this work, we reflect on some questions about the measurement problem in economics and, especially, their relationship with the scientific method. Statistical sources frequently used by economists contain qualitative information obtained from verbal expressions of individuals by means of surveys, and we discuss the reasons why it would be more adequately analyzed with soft methods than with traditional ones. Some comments on the most commonly applied techniques in the analysis of these types of data with verbal answers are followed by our proposal to compute with words. In our view, an alternative use of the well known Income Evaluation Question seems especially suggestive for a computing with words approach, since it would facilitate an empirical estimation of the corresponding linguistic variable adjectives. A new treatment of the information contained in such surveys would avoid some questions incorporated in the so called Leyden approach that do not fit to the actual world.Computing with words, Leyden approach, qualitative answering surveys, fuzzy logic