Stochastic multicriteria acceptability analysis (SMAA) is a multicriteria decision support method for multiple decision makers in discrete problems. In SMAA, the decision makers need not express their preferences explicitly or implicitly. Instead, the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one. Inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis. In this paper we introduce the SMAA-2 method, which extends the original SMAA by considering all ranks in the analysis. In situations where the "elitistic" SMAA may assess large acceptability only for extreme alternatives without sufficient majority support, the more holistic SMAA-2 analysis can be used to identify good compromise candidates. The results are presented graphically. We consider also situations where partial preference information is available. We demonstrate the new method using a real-life decision problem.
In environmental planning and decision processes several alternatives are analyzed in terms of multiple noncommensurate criteria, and many different stakeholders with conflicting preferences are involved. Based on our experience in real-life applications, we discuss how multicriteria decision aid (MCDA) methods can be used successfully in such processes. MCDA methods support these processes by providing a framework for collecting, storing, and processing all relevant information, thus making the decision process traceable and transparent. It is therefore possible to understand and explain why, under several conflicting preferences, a particular decision was made. The MCDA framework also makes the requirements for new information explicit, thus supporting the allocation of resources for the process.
Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision.The computations in SMAA require the evaluation of multidimensional integrals that must in practice be computed numerically. In this paper we present efficient methods for performing the computations through Monte Carlo simulation, analyze the complexity, and assess the accuracy of the presented algorithms. We also test the efficiency of these methods empirically. Based on the tests, the implementation is fast enough to analyze typical-sized discrete problems interactively within seconds. Due to almost linear time complexity, the method is also suitable for analysing very large decision problems, for example, discrete approximations of continuous decision problems.
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