| Provider: | kappalab |
|---|---|
| Version: | 1.0 |
-Contact: Patrick Meyer (patrick.meyer@telecom-bretagne.eu)
-Web page: None
-Reference: P. Meyer, M. Roubens (2005), Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid, in: J. Figueira, S. Greco, and M. Ehrgott, Eds, Multiple Criteria Decision Analysis: State of the Art Surveys, volume 78 of International Series in Operations Research and Management Science, chapter 12, pages 471-506. Springer Science + Business Media, Inc., New York.
Identifies a Mobius capacity by means of an approach called TOMASO in the particular ranking framework. More precisely, given a preorder on the alternatives, and possibly additional linear constraints expressing preferences, importance of criteria, etc., this algorithm determines, if it exists, a capacity minimising the “gap” between the given ranking and the one derived from the Choquet integral, and compatible with the additional linear constraints. The problem is solved by quadratic programming.
Indicates the level of k-additivity of the Mobius capacity (the Mobius transform of subsets whose cardinal is superior to k vanishes).
-Status: define parameter value via XMCDA file or input by hand, by default via XMCDA file.
-Name: kAdditivity
-Constraint description: The value should be a positive integer, less than or equal to the number of criteria.
-Default value: 1
Threshold value indicating the minimal difference in terms of the Choquet integral between two neighbor alternatives in the given ranking.
-Tag: methodParameters
-Code:
<methodParameters> <parameter name="separationThreshold"><!-- REQUIRED --> <value> <real>%1</real> </value> </parameter> </methodParameters>
-Status: define parameter value via XMCDA file or input by hand, by default via input by hand.
-Name: separationThreshold
-Constraint description: The value should be a strictly positive float, less than the highest possible overall value.
A list of criteria. Criteria can be activated or desactivated via the <active> tag (true or false). By default (no <active> tag), criteria are considered as active.
-Tag: criteria
-Code:
<criteria> <criterion> <active>[...]</active> [...] </criterion> [...] </criteria>
A list of alternatives. Alternatives can be activated or desactivated via the <active> tag (true or false). By default (no <active> tag), alternatives are considered as active.
-Tag: alternatives
-Code:
<alternatives> <alternative> <active>[...]</active> [...] </alternative> [...] </alternatives>
A performance table. The evaluations should be numeric values, i.e. <real>, <integer> or <rational>.
-Tag: performanceTable
-Optional: yes, enabled by default
A valued relation on criteria expressing importance constraints on the critera. A numeric <value> indicates a minimal preference threshold for each <pair>. One <pair> represents an affirmation of the type “the Shapley importance index of criterion g1 is greater than the Shapley importance index of criterion g2 with preference threshold delta”.
-Tag: criteriaComparisons
-Optional: yes, enabled by default
A list of <criterionValue> containing the constraints relative to the quantitative importance of the criteria. Each <criterionValue> contains an an <interval>. Each <criteriaValue> represents an affirmation of the type “the Shapley importance index of criterion g1 lies in the interval [a,b]”.
-Tag: criteriaValues
-Optional: yes, enabled by default
A valued relation on pairs of criteria expressing constraints on value of the the Shapley interaction index. A numeric <value> indicates a minimal preference threshold for each <pair> of the relation. One <pair> represents a constraint of the type “the Shapley interaction index of the pair (g1,g2) of criteria is greater than the Shapley interaction index of the pair (g3,g4) of criteria with preference threshold delta”.
-Tag: criteriaComparisons
-Optional: yes, enabled by default
A list of <criterionValue> containing the constraints relative to the type and the magnitude of the Shapley interaction index for pairs of criteria. Each <criterionValue> contains an an <interval>. Each <criteriaValue> represents an affirmation of the type “the Shapley interaction index of the pair (g1,g2) of criteria lies in the interval [a,b]”.
-Tag: criteriaValues
A valued relation relative to the preorder of the alternatives. A numeric <value> indicates a minimal preference threshold for each <pair> of the relation. One <pair> represents a constraint of the type “alternative a is preferred to alternative b with preference threshold delta”.
-Tag: alternativesComparisons
A list of messages generated by the algorithm.
-Tag: methodMessages
The Mobius transform of a capacity.
-Tag: criteriaValues
-Code:
<criteriaValues mcdaConcept="mobiusCapacity"> <criterionValue> <criteriaSet> <element> <criterionID>[...]</criterionID> </element> [...] </criteriaSet> <value> <real>[...]</real> </value> </criterionValue> [...] </criteriaValues>
For further technical details on the web service underlying this program, have a look at its documentation here.