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Using Ordinal Data to Estimate Cardinal Values
Author(s) -
Wang Jingguo,
Zionts Stanley
Publication year - 2014
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.1528
Subject(s) - rank (graph theory) , mathematics , ordinal data , centroid , degree (music) , statistics , surprise , value (mathematics) , computer science , data mining , algorithm , econometrics , artificial intelligence , combinatorics , psychology , social psychology , physics , acoustics
We investigate methods developed in multiple criteria decision‐making that use ordinal information to estimate numerical values. Such methods can be used to estimate attribute weights, attribute values, or event probabilities given ranks or partial ranks. We first review related studies and then develop a generalized rank‐sum (GRS) approach in which we provide a derivation of the rank‐sum approach that had been previously proposed. The GRS approach allows for incorporating the concept of degree of importance (or, difference in likelihood with respect to probabilities and difference in value for attribute values), information that most other rank‐based formulas do not utilize. We then present simulation results comparing the GRS method with other rank‐based formulas such as the rank order centroid method and comparing the GRS methods using as many as three levels of importance (i.e., GRS‐3) with Simos' procedure (which can also incorporate degree of importance). To our surprise, our results show that the incorporation of additional information (i.e., the degree of the importance), both GRS‐3 and Simos' procedure, did not result in better performance than rank order centroid or GRS. Further research is needed to investigate the modelling of such extra information. We also explore the scenario when a decision‐maker has indifference judgments and cannot provide a complete rank order. Copyright © 2014 John Wiley & Sons, Ltd.