# DEX Values

*DEX values* are used throughout DEX models to provide input
values and carry results of evaluations of decision
alternatives. A value that can be assigned to an
attribute is always bound to the context provided by
that attribute’s scale.

A special DEX value *undefined* can be assigned to any attribute, including
those whose scales are undefined. In principle, any operation (aggregation, discretization)
involving *undefined* gives an *undefined* result. However, for qualitative attributes,
DEXi Suite
allows an evaluation mode in which all *undefined* values
are expanded to the full set of the corresponding attribute’s values
prior to evaluation. In this way, *undefined* is interpreted as *unknown*.

DEX values assigned to continuous attributes can only be real (floating-point) numbers. No intervals or other representations of uncertainty are possible.

DEX value types assigned to qualitative attributes are richer and allow expressing uncertainty and imprecision. There are four main qualitative value types: single value, interval, set and value distribution.

For illustrations below, let us take a qualitative scale, consisting of four values: bad, acc, good, excellent.

## Single Values

A *single* DEX value consists of a single element of the corresponding scale.

Example: `acc`

## Interval Values

An *interval value* is defined by two bounds, lower and upper, and consists of all scale elements
between these bounds, including the bounds. An interval is usually denoted `lower:upper`

.

Example: `acc:excellent`

: includes acc, good and excellent

Notational shortcuts are used for preferentially ordered scales:

`<=acc`

: worse than or equal to acc, equivalent to`bad:acc`

`>=acc`

: better than or equal to acc, at least acc, equivalent to`acc:excellent`

## Sets

A *value set* consists of a set of elements of the corresponding scale.
Sets are usually denoted as lists of ;-separated values.
All intervals can be interpreted as sets, while the converse is not always true.

Example: `bad; acc; excellent`

Special notation `*`

is used to denote the full set of values.

Example: `*`

= `bad:excellent`

= `bad; acc; good; excellent`

## Value Distributions

A *value distribution* associates each qualitative scale value with some number, generally
denoted *p* and normally expected to be in the [0,1] interval. Depending on the context and used
evaluation method, *p* can be interpreted as probability or fuzzy set membership.
Distributions are usually displayed in terms of a ;-separated list of pairs `value/p`

.
*p* = 0 is assumed for elements not appearing in the list.

Example: `bad/0.5; good/0.2; excellent/0.3`

(omitted: `acc/0`

)