linProgCapaIdent

Provider:kappalab Version:1.0

Description

-Contact: Patrick Meyer (patrick.meyer@telecom-bretagne.eu)

-Reference: M. Grabisch and M. Roubens (2000), Application of the Choquet Integral in Multicriteria Decision Making, in: Fuzzy Measures and Integrals: Theory and Applications, M. Grabisch, T. Murofushi, and M. Sugeno Eds, Physica Verlag, pages 415-434.

Identifies a Mobius capacity by means of an approach using the linear programming approach proposed by Marichal and Roubens. Roughly speaking, this function determines, if it exists, the capacity compatible with a set of linear constraints that “separates” the most the provided alternatives.

Inputs

kAdditivity

Description:

Indicates the level of k-additivity of the Mobius capacity (the Mobius transform of subsets whose cardinal is superior to k vanishes).

XMCDA related:

-Tag: methodParameters

-Code:

<methodParameters>
    <parameter
         name="kAdditivity"> <!-- REQUIRED  -->
        <value>
            <integer>%1</integer>
        </value>
    </parameter>
</methodParameters>

GUI information:

-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

---

criteria

Description:

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.

XMCDA related:

-Tag: criteria

-Code:

<criteria>
    <criterion>
        <active>[...]</active>
        [...]
    </criterion>
    [...]
</criteria>

---

alternatives

Description:

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.

XMCDA related:

-Tag: alternatives

-Code:

<alternatives>
    <alternative>
        <active>[...]</active>
        [...]
    </alternative>
    [...]
</alternatives>

---

performanceTable

Description:

A performance table. The evaluations should be numeric values, i.e. <real>, <integer> or <rational>.

XMCDA related:

-Tag: performanceTable

---

shapleyPreorder

-Optional: yes, enabled by default

Description:

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”.

XMCDA related:

-Tag: criteriaComparisons

---

shapleyInterval

-Optional: yes, enabled by default

Description:

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]”.

XMCDA related:

-Tag: criteriaValues

---

interactionPreorder

-Optional: yes, enabled by default

Description:

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”.

XMCDA related:

-Tag: criteriaComparisons

---

interactionInterval

-Optional: yes, enabled by default

Description:

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]”.

XMCDA related:

-Tag: criteriaValues

---

alternativesPreorder

Description:

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”.

XMCDA related:

-Tag: alternativesComparisons

---

Outputs

messages

Description:

A list of messages generated by the algorithm.

XMCDA related:

-Tag: methodMessages

---

mobiusCapacity

Description:

The Mobius transform of a capacity.

XMCDA related:

-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.