This dataset is the <code>tt</code> matrix establishing the relation A = D + S, where A = 0:6, D = 0:3 and S = 0:3. The subset made of all the triplets (a,d,s) of (A x D x S) where a = d + s is true has a mass value of 1. To construct the <code>tt</code> matrix, we put the variables A, D, S side by side, as in a truth table representation. Each triplet of the subset is described by a row of the matrix as a vector of zeros and ones.

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Using the Theory of Belief Functions for evidence calculus. Basic probability assignments, or mass functions, can be defined on the subsets of a set of possible values and combined. A mass function can be extended to a larger frame. Marginalization, i.e. reduction to a smaller frame can also be done. These features can be combined to analyze small belief networks and take into account situations where information cannot be satisfactorily described by probability distributions.

Peiyuan Zhu

Using the Theory of Belief Functions

Claude Boivin

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An integer matrix with 18 rows and 17 columns<dl>
 <dt>[1, c(1,2)]</dt>
<dd>value = 0, not used</dd> <dt>[1, 3:17]</dt>
<dd>Identification numbers of the three variables. Column 3 to 9: variable 1; column 10 to 13: variable 2; column 14 to 17: variable 3.</dd> <dt>nospec</dt>
<dd>identification number of the specification</dd> <dt>m</dt>
<dd>the value of the specification, a number between 0 and 1</dd> <dt>6</dt>
<dd>1 if 6 is part of the specification, 0 otherwise</dd> <dt>5</dt>
<dd>1 if 5 is part of the specification, 0 otherwise</dd> <dt>4</dt>
<dd>1 if 4 is part of the specification, 0 otherwise</dd> <dt>3</dt>
<dd>1 if 3 is part of the specification, 0 otherwise</dd> <dt>2</dt>
<dd>1 if 2 is part of the specification, 0 otherwise</dd> <dt>1</dt>
<dd>1 if 1 is part of the specification, 0 otherwise</dd> <dt>0</dt>
<dd>1 if 0 is part of the specification, 0 otherwise</dd> 
</dl>

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The Captain's Problem. ads: Relation between variables Arrival (A), Departure delay (D) and Sailing delay (S) — ads

An integer matrix with 18 rows and 17 columns<dl>
 <dt>[1, c(1,2)]</dt>
<dd>value = 0, not used</dd>

 <dt>[1, 3:17]</dt>
<dd>Identification numbers of the three variables. Column 3 to 9: variable 1; column 10 to 13: variable 2; column 14 to 17: variable 3.</dd>

 <dt>nospec</dt>
<dd>identification number of the specification</dd>

 <dt>m</dt>
<dd>the value of the specification, a number between 0 and 1</dd>

 <dt>6</dt>
<dd>1 if 6 is part of the specification, 0 otherwise</dd>

 <dt>5</dt>
<dd>1 if 5 is part of the specification, 0 otherwise</dd>

 <dt>4</dt>
<dd>1 if 4 is part of the specification, 0 otherwise</dd>

 <dt>3</dt>
<dd>1 if 3 is part of the specification, 0 otherwise</dd>

 <dt>2</dt>
<dd>1 if 2 is part of the specification, 0 otherwise</dd>

 <dt>1</dt>
<dd>1 if 1 is part of the specification, 0 otherwise</dd>

 <dt>0</dt>
<dd>1 if 0 is part of the specification, 0 otherwise</dd>

 
</dl>

ads: The Captain's Problem. `ads`: Relation between variables Arrival (A), Departure delay (D) and Sailing delay (S)

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