PrometheePreferenceWithInteractions

Provider:PUT
Version:1.0.0

Description

Computes aggregated preference indices with interactions between criteria The key feature of this module is its flexibility in terms of the types of elements allowed to compare, i.e. alternatives vs alternatives, alternatives vs boundary profiles and alternatives vs central (characteristic) profiles. Each criterion can have its own preference function (one of six predefined functions).

Inputs

(For outputs, see below)

criteria

Description:

Criteria to consider, possibly with preference and indifference thresholds. For Gaussian function it needs inflection point (sigma). Each criterion must have a preference direction specified (min or max). It is worth mentioning that this module allows to define thresholds as constants as well as linear functions.

alternatives

Description:

Alternatives to consider.

XMCDA related:

  • Tag: alternatives

performance table

Description:

The performance of alternatives.

XMCDA related:

  • Tag: performanceTable

profiles performance table

Optional: yes, enabled by default

Description:

The performance of profiles (boundary or central).

XMCDA related:

  • Tag: performanceTable

weights

Description:

Weights of criteria to consider.

XMCDA related:

  • Tag: criteriaValues

generalised criteria

Optional: yes, enabled by default

Description:

ID number of predefined preference function specified for each criterion.

XMCDA related:

  • Tag: criteriaValues

interactions

Description:

Declarations of criteria interactions which should be taken into account. Possible interactions are: “strengthening”, “weakening” and “antagonistic”.

Every such declaration contains a pair of criteria and a numerical value for the interaction coefficient. This value should be negative for “weakening” and positive for “strenghtening” and “antagonistic”. This coefficient should be interpreted as follows: the larger its absolute value, the more important the interaction effect. All interaction coefficients should fulfill positive net balance condition.

The order in which each criterion appears in its interaction definition is significant for antagonistic interactions (it designates the direction in which certain criterion affects the other). For strengthening and weakening order is not important. (Coefficients k_ij = k_ji and only one of this is needed).

There are no limits on the number of interactions that can be declared, but keep in mind that it should be rather small to make sense.

It is possible to declare more than one interactions of the same type, although please note that considering the same pair of criteria involved, the “strengthening” and “weakening” interactions are mutually exclusive.

XMCDA related:

  • Tag: criteriaValues
  • Code:
<criteriaValues mcdaConcept=”criteriaInteractions”>
<criterionValue mcdaConcept=”strengthening”>
<criteriaSet>
<element>
<criterionID>c01</criterionID>

</element> <element>

<criterionID>c02</criterionID>

</element>

</criteriaSet> <value>

<real>9.5</real>

</value>

</criterionValue> <criterionValue mcdaConcept=”antagonistic”>

<criteriaSet>
<element>
<criterionID>c02</criterionID>

</element> <element>

<criterionID>c04</criterionID>

</element>

</criteriaSet> <value>

<real>0.01</real>

</value>

</criterionValue>

</criteriaValues>


categories profiles

Optional: yes, enabled by default

Description:

Definitions of central or boundary profiles connected with classes (categories)

XMCDA related:

  • Tag: categoriesProfiles

method parameters

Description:

First parameter specifies the type of elements provided for comparison.

Choosing ‘boundary_profiles’ or ‘central_profiles’ requires providing inputs ‘classes_profiles’ and ‘profiles_performance_table’ as well (which are optional by default).

Second parameter specifies the type of function used for comparison of each criterion. Choosing ‘specified’ requires providing inputs “generalised_criterion” which is optional by default. Choosing some of numbers sets same function for all criteria. Third parameter specifies type of Z function in computing criteria interaction effect.

GUI information:

  • Parameter values can be defined via the GUI or the XMCDA file, by default via GUI.

  • Name: comparison with

    • Type: drop-down list
    • Possible values:
      • alternatives vs alternatives (XMCDA label : alternatives) (default)
      • alternatives vs boundary profiles (XMCDA label : boundary_profiles)
      • alternatives vs central (characteristic) profiles (XMCDA label : central_profiles)
  • Name: generalised criterion

    • Type: drop-down list
    • Possible values:
      • Each criterion needs its own function (XMCDA label : specified) (default)
      • Usual Criterion (XMCDA label : usual)
      • U-Shape Criterion, needs indifference threshold specified in criterion. (XMCDA label : u-shape)
      • V-Shape Criterion, needs threshold of strict preference specified in criterion. (XMCDA label : v-shape)
      • Level Criterion, needs both indifference and strict preference thresholds specified in criterion. (XMCDA label : level)
      • V-Shape with Indifference Criterion, needs both indifference and strict preference thresholds specified in criterion. (XMCDA label : v-shape-ind)
      • Gaussian Criterion, needs the inflection point of the preference function specified in criterion. (XMCDA label : gaussian)
  • Name: z function

    Z(x, y) - function used to capture interaction effects in the ambiguity zone. There are multiple forms that can be chosen for it, but two of them have intuitive and meaningful interpretation: Z(x, y) = min{x, y} Z(x, y) = xy - the last one is prefereable, though.

    • Type: drop-down list
    • Possible values:
      • Z(x, y) = xy (XMCDA label : multiplication) (default)
      • Z(x, y) = min{x, y} (XMCDA label : minimum)

XMCDA related:

  • Tag: methodParameters

  • Code:

    <methodParameters>
      <parameter name="comparison_with">
        <value>
          <label>%1</label>
        </value>
      </parameter>
      <parameter name="generalised_criterion">
        <value>
          <label>%2</label>
        </value>
      </parameter>
      <parameter name="z_function">
        <value>
          <label>%3</label>
        </value>
      </parameter>
    </methodParameters>
    

Outputs

preferences

Description:

Aggregated preference matrix computed from the given data. This matrix aggregates partial preference indices from all criteria into single preference index per pair of alternatives or alternatives/profiles.

XMCDA related:

  • Tag: alternativesComparisons

partial preferences

Description:

Preference matrix computed from the given data. This matrix contains partial preference indices for all criteria and all pairs of alternatives or alternatives/profiles.

XMCDA related:

  • Tag: alternativesComparisons

messages

Description:

Messages or errors generated by this module.

XMCDA related:

  • Tag: methodMessages

For further technical details on the web service underlying this program, have a look at its documentation here.