# Types of Set

A set is a collection of unique elements. In AIMMS, a set is finite. When you declare a set in AIMMS, it is one of the following:

Root set

Calendar

Subset

Relation

## Root Set

A collection of explicit names is called a root set.

For instance, the set `s_Weathertypes = { Rainy, Cloudy, Sunny }`

is a root set.

```
1Set s_WeatherTypes {
2 Index: i_WeatherType;
3 Parameter: ep_WeatherType;
4 Definition: data { Rainy, Cloudy, Sunny };
5}
```

The elements of this set are `Rainy`

, `Cloudy`

, and `Sunny`

.
Note that the elements of a root set do not need to be specified in the model, they can be read in when the model is running; for instance from a database.

## Calendar

A collection of dates is called a calendar.

A calendar is also a root set.

For instance the calendar `cal_ThisWeek`

is declared as:

```
1Calendar cal_ThisWeek {
2 Index: i_dayThisWeek;
3 Parameter: ep_dayThisWeek;
4 Unit: day;
5 BeginDate: "2020-02-17";
6 EndDate: "2020-02-23";
7 TimeslotFormat: "%c%y-%m-%d";
8}
```

With this declaration, the calendar `cal_ThisWeek`

contains the elements `2020-02-17`

, `2020-02-18`

, `2020-02-19`

, `2020-02-20`

, `2020-02-21`

, `2020-02-22`

, and `2020-02-23`

.

Note that the `BeginDate`

, `EndDate`

, and `TimeslotFormat`

need not be explicit strings, but string parameters can be used as well.

## Subset

A collection of elements, which are also elements of a root set (or calendar), is called a subset.

For instance, the set `s_DryWeatherTypes`

is a subset of `s_WeatherTypes`

and declared as follows:

```
1Set s_DryWeatherTypes {
2 SubsetOf: s_WeatherTypes;
3 Index: i_DryWeatherType;
4 Parameter: ep_DryWeatherType;
5 Definition: data { Cloudy, Sunny };
6}
```

A subset is not a root set. But like root sets, the data for a subset need not be specified in the model, but can be read in at runtime.

## Relation

A collection of tuples, in which each component is an element of another set, is called a relation.

Observations can be modeled as a relation, for instance as follows:

```
1Set s_ThisWeeksWeather {
2 SubsetOf: (cal_ThisWeek,s_WeatherTypes);
3 Definition: {
4 data
5 { ( 2020-02-17, Cloudy ), ( 2020-02-18, Sunny ),
6 ( 2020-02-19, Cloudy ), ( 2020-02-20, Sunny ),
7 ( 2020-02-21, Rainy ), ( 2020-02-22, Rainy ),
8 ( 2020-02-23, Rainy ) }
9 }
10}
```

In this example, `( 2020-02-17, Cloudy )`

is a tuple.
Also `2020-02-17`

is a component in a tuple, and it is an element of the set `cal_ThisWeek`

.

### Simple Sets vs. Relations

A root set, a calendar and a subset are all simple sets. A relation is not a simple set. For a simple set, you can declare: zero, one, or more indices; and zero, one, or more element parameters.

### Compound Sets

A set that is both a relation and a simple set, is called a compound set.
**Compound sets are no longer supported.** See Overview: Deprecation of Compound Sets.