Attributes

Attributes are variables that occur in multi-criteria models. They are organized into a hierarchical structure called tree of attributes. According to their position in the tree, the attributes are either:

  • basic attributes: terminal nodes (“leaves”) of the tree, or

  • aggregate attributes: internal nodes in the tree.

Basic attributes represent inputs of the DEX model. Alternatives are described by the values of basic attributes.

Some basic attributes can be “linked” in order to structure the model as a full hierarchy rather than a tree.

Aggregate attributes represent evaluations of alternatives. They include one or more roots of the tree, which represent the overall evaluation of alternatives.

In DEXi Suite, each attribute is defined by its:

  • Name: main identification of the attribute, which is typically a short string used in printouts, table headings, etc.

  • Description: usually a longer string providing further documentation about the attribute

  • Scale

Aggregate attributes also have associated an aggregation or discretization function.

Linked Attributes

In principle, DEX models have a strict tree structure: attributes are structured so that there is exactly one path from each aggregate attribute to the root of the tree. This means that each attribute, other than the root, influences exactly one parent in the tree. Sometimes, this is not enough and we wish to introduce attributes that influence more than one parent. In other words, we wish to create attribute hierarchies (directed acyclic graphs) rather than ordinary trees.

For this purpose, DEXi Suite uses the concept of linked attributes. The idea is that whenever there are two attributes in the tree that have equal names and equal scales, and at least one of them is basic, they are declared ‘linked’ and they in a logical sense represent a single attribute. Attribute linking is done automatically by DEXiWin, but only when enabled explicitly in preference settings. By default, linking is disabled and equally named attributes are considered different.

This concept allows that DEX models still retain their basic tree structure. In tree displays, linked attributes appear separately, so the tree structure is preserved. However, when defining alternatives, linked attributes appear only once and require only a single data entry.

Terminological Remarks

In MCDM, the definitions of terms goal, objective, criterion, attribute, performance variable, indicator vary to some extent depending on the context, author and method. These terms all refer to “something” that needs to be achieved by a proper decision and has to be in some way considered in the corresponding decision model. Specifically, the terms criterion and attribute are sometimes considered equivalent, while some other authors understand criterion only as a preferentially ordered attribute.

In DEXi Suite, the term attribute is used as a general term for all variables occurring in a DEX model. This is because the preference order of an attribute is known only after it has been associated with a scale, which can occur much later than defining the attribute itself. According to some strict definitions, the attribute can be understood as a criterion only when assigned an ordered scale. Thus, in general terms, DEX models consist of attributes, and are often referred to as multi-attribute models.