Scale

Scale represents a set of values that can be assigned to an attribute.

In DEXi, scales are qualitative and discrete. They consist of a set of words, such as: ‘excellent’, ‘acceptable’, ‘inappropriate’, etc.

Scales can be ordered or unordered, and ordered scales can be either increasing or decreasing. An unordered scale is just a collection of values, whose relation with each other is unknown or undefined. In contrast, the values of an ordered scale are ordered preferentially, that is, according to their contribution to the quality of options. The values of increasing scales are ordered from ‘bad’ to ‘good’ values, and the value of a decreasing scales are ordered from ‘good’ to ‘bad’ values. In both cases, ‘bad’ represents a value that is disadvantageous for the option and is least preferred by the decision maker. Analogously, ‘good’ represents an advantageous and most preferred value. The ordering of scales plays an important role in the definition of utility functions, where it simplifies the definition of decision rules and facilitates checking of their consistency.

With ordered scales, the lowest value is considered ‘bad’ and the highest ‘good’ by default. This can be changed in Scale Editor, where you can individually declare the status of each value. In this way, not only a single value, but a whole subsequence of values can be declared as ‘bad’ or ‘good’.

For emphasis and better visualization, extreme values of ordered scales are printed in different fonts and colors. By default, ‘bad’ values appear in bold-red and ‘good’ values appear in italic-green. These can be changed in Settings/Report.

Example scales

no, yes
low, medium, high (e.g., for “Quality”)
high, medium, low (e.g., for “Price”)
unacceptable, acceptable, good, excellent

Recommendations

On scale size (number of values):

  • For basic attributes: Use the least number of values that is still sufficient to distinguish between importantly different characteristics of options. Usually, this means two to four values.

  • For aggregate attributes: The number of values should gradually increase from basic attributes towards the root of tree of attributes. For example, three four-valued attributes might be aggregated into a five-valued attribute. Five-valued root attributes usually work quite well.

On scale ordering:

  • Use increasing scales whenever possible, they really help in the definition of utility functions.

  • Avoid decreasing scales. They are much less comprehensible than increasing scales. Increasing and decreasing scales do not work when mixed together in a single utility function.

See also

DEXi’s Scale Editor.

Scales in the Car Evaluation model.