Comparing principal component analysis and multidimensional scaling for the representation of PROMETHEE results

Q4 Business, Management and Accounting

International Journal of Multicriteria Decision Making Pub Date : 2016-01-09 DOI:10.1504/ijmcdm.2015.074089

Bastian Schmidtmann, Genoveva Schmidtmann

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引用次数: 0

Abstract

In this paper, we present a new method of visualising the results of PROMETHEE and a comparison of the new method with the common GAIA method (Mareschal and Brans, 1988) and reveal its application in the context of choice for alternative vehicles. Visualisation methods make the impact of each single criterion and its weight on every single alternative visible. The most common method for visualising the results of PROMETHEE models is the GAIA method. To evaluate if GAIA itself or visualisation methods themselves are difficult to handle for the decision maker a new visualisation method for PROMETHEE results is developed and compared with the GAIA method. The method we introduce in this paper is based on the classical multidimensional scaling (MDS) (Chatfield and Collins, 1980). MDS is extended by property fitting to integrate each single criterion into the visualisation (Homburg and Krohmer, 2009). We compare the results by applying the procrustes analysis (Gower and Dijksterhuis, 2004). Finally, we give an outlook of future research aspects on the comparison and the new visualisation method in particular.

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比较主成分分析和多维标度对PROMETHEE结果表示的影响

在本文中，我们提出了一种将PROMETHEE结果可视化的新方法，并将新方法与常见的GAIA方法(Mareschal和Brans, 1988)进行了比较，并揭示了其在替代车辆选择方面的应用。可视化方法使每个单一标准的影响及其对每个单一替代方案的权重可见。将PROMETHEE模型的结果可视化的最常用方法是GAIA方法。为了评估GAIA本身或可视化方法本身是否难以为决策者处理，开发了一种新的PROMETHEE结果可视化方法，并与GAIA方法进行了比较。本文介绍的方法是基于经典的多维标度(MDS) (Chatfield and Collins, 1980)。MDS通过属性拟合进行扩展，将每个单一标准集成到可视化中(Homburg和Krohmer, 2009)。我们通过应用procrustes分析来比较结果(Gower和Dijksterhuis, 2004)。最后，我们对未来的研究方向进行了展望，特别是对新的可视化方法进行了展望。

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来源期刊

International Journal of Multicriteria Decision Making Business, Management and Accounting-Strategy and Management

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： IJMCDM is a scholarly journal that publishes high quality research contributing to the theory and practice of decision making in ill-structured problems involving multiple criteria, goals and objectives. The journal publishes papers concerning all aspects of multicriteria decision making (MCDM), including theoretical studies, empirical investigations, comparisons and real-world applications. Papers exploring the connections with other disciplines in operations research and management science are particularly welcome. Topics covered include: -Artificial intelligence, evolutionary computation, soft computing in MCDM -Conjoint/performance measurement -Decision making under uncertainty -Disaggregation analysis, preference learning/elicitation -Group decision making, multicriteria games -Multi-attribute utility/value theory -Multi-criteria decision support systems and knowledge-based systems -Multi-objective mathematical programming -Outranking relations theory -Preference modelling -Problem structuring with multiple criteria -Risk analysis/modelling, sensitivity/robustness analysis -Social choice models -Theoretical foundations of MCDM, rough set theory -Innovative applied research in relevant fields