Optimization under ordinal scales: When is a greedy solution optimal?

1997 ◽  
Vol 46 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Aleksandar Pekeč
2002 ◽  
Vol 7 (3) ◽  
pp. 4-5

Abstract Different jurisdictions use the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) for different purposes, and this article reviews a specific jurisdictional definition in the Province of Ontario of catastrophic impairment that incorporates the AMA Guides. In Ontario, a whole person impairment (WPI) exceeding 54% or a mental or behavioral impairment of Class 4 or 5 qualifies the individual for catastrophic benefits, and individuals who do not meet the test receive a lesser benefit. By inference, this establishes a parity threshold among dissimilar injuries and dissimilar outcome assessment scales for benefits. In Ontario, the Glasgow Coma Scale (GCS) identifies patients who have a high probability of death or of severely disabled survival. The GCS recognizes gradations of vegetative state and disability, but translating the gradations for rating individual impairment on ordinal scales into a method of assessing percentage impairments cannot be done reliably, as explained in the AMA Guides, Fifth Edition. The AMA Guides also notes that mental and behavioral impairment in Class 4 (marked impairment) or 5 (extreme impairment) indicates “catastrophic impairment” by significantly impeding useful functioning (Class 4) or significantly impeding useful functioning and implying complete dependency on another person for care (Class 5). Translating the AMA Guides guidelines into ordinal scales cannot be done reliably.


Author(s):  
BERNARD DE BAETS ◽  
JÁNOS FODOR ◽  
DANIEL RUIZ-AGUILERA ◽  
JOAN TORRENS

In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.


2008 ◽  
Vol 57 (6) ◽  
pp. 825-834 ◽  
Author(s):  
Magnus Bordewich ◽  
Allen G. Rodrigo ◽  
Charles Semple
Keyword(s):  

2007 ◽  
Vol 16 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Henry J. Gardner ◽  
Michael A. Martin

Likert scaled data, which are frequently collected in studies of interaction in virtual environments, demand specialized statistical tools for analysis. The routine use of statistical methods appropriate for continuous data in this context can lead to significant inferential flaws. Likert scaled data are ordinal rather than interval scaled and need to be analyzed using rank based statistical procedures that are widely available. Likert scores are “lumpy” in the sense that they cluster around a small number of fixed values. This lumpiness is made worse by the tendency for subjects to cluster towards either the middle or the extremes of the scale. We suggest an ad hoc method to deal with such data which can involve a further lumping of the results followed by the application of nonparametric statistics. Averaging Likert scores over several different survey questions, which is sometimes done in studies of interaction in virtual environments, results in a different sort of lumpiness. The lumped variables which are obtained in this manner can be quite murky and should be used with great caution, if at all, particularly if the number of questions over which such averaging is carried out is small.


2004 ◽  
Vol 48 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Dieter Denneberg ◽  
Michel Grabisch
Keyword(s):  

2013 ◽  
Vol 56 (4) ◽  
pp. 313-322 ◽  
Author(s):  
Diane Sellers ◽  
Lindsay Pennington ◽  
Anne Mandy ◽  
Christopher Morris

2015 ◽  
Vol 41 (3) ◽  
pp. 355-383 ◽  
Author(s):  
Nelly Barbot ◽  
Olivier Boëffard ◽  
Jonathan Chevelu ◽  
Arnaud Delhay

Linguistic corpus design is a critical concern for building rich annotated corpora useful in different domains of applications. For example, speech technologies such as ASR (Automatic Speech Recognition) or TTS (Text-to-Speech) need a huge amount of speech data to train data-driven models or to produce synthetic speech. Collecting data is always related to costs (recording speech, verifying annotations, etc.), and as a rule of thumb, the more data you gather, the more costly your application will be. Within this context, we present in this article solutions to reduce the amount of linguistic text content while maintaining a sufficient level of linguistic richness required by a model or an application. This problem can be formalized as a Set Covering Problem (SCP) and we evaluate two algorithmic heuristics applied to design large text corpora in English and French for covering phonological information or POS labels. The first considered algorithm is a standard greedy solution with an agglomerative/spitting strategy and we propose a second algorithm based on Lagrangian relaxation. The latter approach provides a lower bound to the cost of each covering solution. This lower bound can be used as a metric to evaluate the quality of a reduced corpus whatever the algorithm applied. Experiments show that a suboptimal algorithm like a greedy algorithm achieves good results; the cost of its solutions is not so far from the lower bound (about 4.35% for 3-phoneme coverings). Usually, constraints in SCP are binary; we proposed here a generalization where the constraints on each covering feature can be multi-valued.


Sign in / Sign up

Export Citation Format

Share Document