The Hellinger distance in Multicriteria Decision Making: An illustration to the TOPSIS and TODIM methods

• Published in: Expert systems with applications Vol. 41; no. 9; pp. 4414 - 4421
• Main Authors: Lourenzutti, Rodolfo, Krohling, Renato A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.07.2014; Elsevier
• Subjects: Acronyms; Applied sciences; Computer science; control theory; systems; Data processing. List processing. Character string processing; Decision making; Decision theory. Utility theory; Dominance; Exact sciences and technology; Expert systems; Hellinger distance; Information systems. Data bases; Interactive; Linear inference, regression; Mathematics; Memory organisation. Data processing; Multicriteria Decision Making (MCDM); Operational research and scientific management; Operational research. Management science; Probability and statistics; Probability distribution; Sciences and techniques of general use; Software; Statistics; Stochastic dominance degree; Stochasticity; TODIM; TOPSIS; Transformations; Hellinger distance; TODIM; Probability distribution; Multicriteria Decision Making (MCDM); TOPSIS; Stochastic dominance degree; Real number; Decision support system; Multicriteria analysis; Decision making; Data transformation; Partial ordering; Decision analysis; Modeling; Stochastic dominance; Portuguese; Acronym
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2014.01.015

•We brought the Hellinger distance to the context of Multicriteria Decision Making.•We adapted the TOPSIS and TODIM methods to directly process probability distributions.•Both methods were illustrated in two examples with promising results. Due to the difficulty in some situations of expressing the ratings of alternatives as exact real numbers, many well-known methods to support Multicriteria Decision Making (MCDM) have been extended to compute with many types of information. This paper focuses on the information represented as probability distribution. Many of the methods that deal with probability distribution use the concept of stochastic dominance, which imposes very strong restrictions to differentiate two probability distributions, or uses the probability distributions to obtain a quantity that will be used to rank the alternatives. This paper brings the Hellinger distance concept to the MCDM context to assist the models to deal with probability distributions in a direct way without any transformation. Transformations in the data or summary quantities may miss represent the original information. For direct comparisons among probability distributions we use the stochastic dominance degree (SDD). We illustrate how simple it can be to adapt the existing methods to deal with probability distributions through the Hellinger distance and SDD by adapting the TOPSIS and TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) methods.