# Overview: types of Set¶

A set is a collection of unique elements. In AIMMS, a set is finite.

## Types of Sets¶

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.

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

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:

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

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:

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

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:

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

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.

Last Updated: February, 2020