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عنوان فارسی مقاله:

عدم قطعیت مدل سازی در تحلیل پذیری چند ضلعی تصادفی

عنوان انگلیسی مقاله:

Modelling uncertainty in stochastic multicriteria acceptability analysis

سال انتشار : 2016

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2. Notation and background

 Consider a decision problem consisting of I alternatives fa1; a2 ,…, aIg evaluated on J attributes fc1; c2; …; cJg. Let Zij be a random variable denoting the attribute evaluation of ai on cj , and U be a multi-attribute utility function mapping the attribute evaluations of alternative ai (denoted Zi) to a real value using a weight vector w. A joint density function f XðZÞ governs the generation of the Zij in the space XDRIJ , and a second joint density function gðwÞ governs the generation of imprecise or unknown weights in the weight space W. Total lack of knowledge is usually represented by a uniform distribution in W. If restrictions have been placed on W we denote the feasible weight space by W0 . The original SMAA method [20] analysed the combinations of attribute weights that result in each of a set of alternatives being selected when using an additive utility function. Subsequently, a number of SMAA variants have been developed. These differ in terms of the preference model used and thus the type of preference information that is imprecisely known, but are all based upon Monte Carlo simulation from distributions which govern unknown preference parameters (and attribute evaluations). For example, SMAA variants are available for value function [20,17], outranking [10], reference point [21,5], prospect theory [18], Choquet integral [2], and AHP [7] methods. Comprehensive reviews are given by Tervonen and Figueira [25] and Lahdelma and Salminen [19]. Given a particular weight vector w, the global utility of each alternative can be computed and a rank ordering of alternatives obtained. SMAA-2 [17] is based on simulating a large number of random weight vectors from gðwÞ and observing the proportion and distinguishing features of weight vectors which result in each alternative obtaining a particular rank r (usually the “best” rank, r¼1), using an additive value function model. Let the set of weight vectors that result in alternative ai obtaining rank r be denoted by Wi r . SMAA is based on an analysis of these sets of weights using a number of descriptive measures, the most important of which are: Acceptability indices: The rank-r acceptability index bi r measures the proportion of all simulation runs, i.e. weight vectors, that make alternative ai obtain rank r. A cumulative form of the acceptability index called the R-best ranks acceptability index is defined as BR i ¼ PR r ¼ 1 br i and measures the proportion of all weight vectors for which alternative ai appears anywhere in the best R ranks. In the discussion in Section 5 we make use of ordered acceptability indices, where we denote the alternative with the k-th largest rank-r acceptability index by ar ðkÞ , and its acceptability index by br ðkÞ. Central weight vectors: The central weight vector wc i is defined as the expected center of gravity of the favourable weight space Wi 1 . It gives a concise description of the “typical” preferences supporting the selection of a particular alternative ai, and in practice is computed from the empirical (element-wise) averages of all weight vectors supporting the selection of ai as the best alternative.

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کلمات کلیدی:

A survey on stochastic multicriteria acceptability analysis methods ... onlinelibrary.wiley.com/doi/10.1002/mcda.407/abstract by T Tervonen - ‎2008 - ‎Cited by 143 - ‎Related articles Nov 19, 2007 - Stochastic multicriteria acceptability analysis (SMAA) comprises a family of ... including incomplete, imprecise, and uncertain information. Multi-criteria dynamic decision under uncertainty: a stochastic viability ... https://www.ncbi.nlm.nih.gov/pubmed/19084541 by M De Lara - ‎2009 - ‎Cited by 67 - ‎Related articles Math Biosci. 2009 Feb;217(2):118-24. doi: 10.1016/j.mbs.2008.11.003. Epub 2008 Nov 24. Multi-criteria dynamic decision under uncertainty: a stochastic ... A Review and Classification of Approaches for Dealing with ... https://www.ncbi.nlm.nih.gov › NCBI › Literature › PubMed Central (PMC) by H Broekhuizen - ‎2015 - ‎Cited by 29 - ‎Related articles Jan 29, 2015 - Multi-criteria decision analysis (MCDA) is increasingly used to support decisions ... [15] define four types of uncertainty: stochastic uncertainty, ... [PDF]Uncertainty Analysis Methods For Multi-Criteria Decision Analysis https://digital.library.adelaide.edu.au/dspace/bitstream/2440/63152/8/02whole.pdf by KM Hyde - ‎2006 - ‎Cited by 14 - ‎Related articles Decision Analysis) present the stochastic uncertainty analysis approach and ... PROMETHEE MCDA Method, Journal of Multi-Criteria Decision Analysis,. Vol 12 ... Prospect theory and stochastic multicriteria acceptability analysis ... https://www.researchgate.net/.../221997707_Prospect_theory_and_stochastic_multicriter... Stochastic multicriteria acceptability analysis (SMAA) is a family of multicriteria decision support methods that allows representing inaccurate, uncertain, or partly ...