Some metrological aspects of preferences expressed by prioritization of alternatives

Vanacore, Amalia; Marmor, Yariv N.; Bashkansky, Emil

doi:10.1016/j.measurement.2018.11.012

Cited by 12 publications

(12 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we restrict ourselves to strict ranking/prioritization only, when ranking and prioritization mean the same thing. We focus on only two metrics: the Kendall τ distance 16 and geodesic distance 5 . When n is a size of the PC (or list), there are n ! feasible PCs/lists, according to the number of possible permutations.…”

Section: Suggested Methods For Overcoming Problemsmentioning

confidence: 99%

“…According to Vanacore et al, 5 all feasible PCs are scattered on the surface of the n ( n − 1)/2‐dimensional sphere. If one of them, for example, the naturally ordered chain C 0 : A 1 > A 2 > A 3 > ··· > A n , is considered as a base (north pole [N]), then the reverse chain is located on the south pole [S] of this sphere and all the remaining ( n !…”

Section: Suggested Methods For Overcoming Problemsmentioning

confidence: 99%

“…There are n ! strict PCs (according to number of permutations) and many more tied PCs 5 . Note that the construction of a chain is based only on relationships among the predetermined alternatives, without necessarily being related to the evaluation of the property under study on some ordinal scale.…”

Section: Types Of Data and Their Descriptionmentioning

confidence: 99%

See 2 more Smart Citations

Processing new types of quality data

Marmor

Bashkansky

2020

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

Quality engineers are increasingly faced with the need to deal with new types of data, which are significantly different from ordinary numerical data by virtue of their nature and the operations that can be performed with them. Basic concepts related to processing of such data, ie, data similarity, measurement system analysis, variation analysis, and data fusion, need to be thoroughly rethought. Reviewing recent publications in the field, we suggest a common approach to processing all data types on the basis of the idea of defining the distance metric for the appropriate data space. The article discusses six types of quality data (nominal, ordinal, preference chains, strings, tree structured, and product/process distribution) and four data processing aspects (calculating data similarity, error description, data fusion, and intradispersion and interdispersion studies). Necessary information and recommendations are given for each combination of data type and problem. They are also summarized in a table that refers the reader to various sections of the article. Any other data type for which the distance metric is definable can be included into the framework of the proposed unified approach.

show abstract

Section: Suggested Methods For Overcoming Problemsmentioning

confidence: 99%

Section: Suggested Methods For Overcoming Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Processing new types of quality data

Marmor

Bashkansky

2020

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…Starting from the cosine similarity (Equation ), a measure of dissimilarity is the angular distance, expressed as the angle between the Euclidian vectors

\overset{a}{true}

and

\overset{b}{true}

normalized to the maximum distance, π, corresponding to vectors having opposite direction:

L ((),, \overset{true\to}{a}, \overset{true\to}{b}) = \frac{{\overset{θ}{true}}_{\overset{true\to}{a}, \overset{true\to}{b}}}{π} = \frac{arccos ((), \frac{\sum_{i = 1}^{n} a_{i} \cdot b_{i}}{\sqrt{\sum_{i = 1}^{n} a_{i}^{2}} \cdot \sqrt{\sum_{i = 1}^{n} b_{i}^{2}}})}{π} .

…”

Section: Methodsmentioning

confidence: 99%

“…Following the multidimensional geometry approach, in this paper consumer PCs are analyzed and interpreted using a simple distance metric based on cosine similarity . Specifically, the average distance between the PCs expressed by any two consumers on the same set of n alternatives is assumed as a measure of “reproducibility” of consumer preferences; whereas the average distance over the PCs expressed at different points in time by the same consumer (eg, test‐retest experiments) is assumed as a measure of “repeatability” of consumer preferences.…”

Section: Introductionmentioning

confidence: 99%

Analysis of consumer preferences expressed by prioritization chains

Vanacore

Pellegrino

Marmor

et al. 2019

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

In this paper, a novel approach is proposed to analyze and interpret consumer preference data expressed as weak orderings (ie, preference chains) over a set of alternatives. A simple distance metric based on cosine similarity is used to assess the repeatability and reproducibility of consumer preferences. These concepts have been borrowed from metrology and can be usefully adopted to evaluate the meaningfulness of aggregated measures (eg, median preference chain) defined over the preference data set. The proposed approach is fully exploited through a real case study involving a group of consumers expressing their preferences over alternative types of pizza toppings.

show abstract