TBMLib 0.1.0

Transferable Belief Model (TBM)

This library implements some TBM functions for transforming bbas along with some normalization, combination, discounting rules and others. More information and references on TBM can be found on Wikipedia.

License : LGPL V2.1

BBA transformations

These functions have been ported from Philippe Smets Matlab functions (link). Some examples are provided below. Please refer to the unit tests for a complete overview.

//BBA m to commonality Q  
    double[] m = { 0.09, 0.3, 0.6, 0.01 };
    double[] q = BeliefFunctions.Instance.MtoQ(m);
    // q = {1.0, 0.31, 0.61, 0.01}

//BBA m to probabilities  
    double[] m = { 0.09, 0.3, 0.6, 0.01 };
    double[] betp = BeliefFunctions.Instance.BetP(m);
    // betp = {0.335, 0.664}

BBAs combination rules

The library implements the Conjunctive Rule of Combination (CRC), the Disjunctive Rule of Combination (DRC), the Cautious Conjunctive rule of Combination (CCRC) and the Bold Disjunctive Rule of Combination (BDRC). See the following publication for more details.

Thierry Denœux (2008). Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artificial Intelligence, Volume 172, Issues 2–3, February 2008, Pages 234-264

Examples:

//CRC combination rule  
    double[] m = { 0.09, 0.3, 0.6, 0.01 };
    ICombinationStrategy strategy = new CRC<NoNormalization>();
    double[] m = strategy.Combine(m, m, out double[] pre_normalization);
    // m = {0.5319, 0.0960, 0.3720, 0.0001}

BBA normalization rules

The library implements Dempster, Yager and Dubois-Prade normalization rules. See the following publication for more details.

Arnaud Martin, Christophe Osswald, Jean Dezert, and Florentin Smarandache (2008). General combination rules for qualitative and quantitative beliefs.

Examples:

//Dubois-Prade normalization rule  
    double[] m1 = { 0.0, 0.5421, 0.2953, 0.0, 0.0924, 0.0, 0.0, 0.0702 };
    double[] m2 = { 0.0, 0.2022, 0.6891, 0.0, 0.0084, 0.0, 0.0, 0.1003 };
    ICombinationStrategy strategy = new CRC<DuboisPradeNormalizationStrategy>();
    double[] m = strategy.Combine(m1, m2, out double[] pre_normalization);
    // m = {0.0, 0.178, 0.281, 0.433, 0.01, 0.023, 0.066, 0.007}

BBA discounting

The library implements the classical discounting (all hypothesis are discounted by a common factor) and the contextual discounting (a discounting factor is associated with each hypothesis). See the following publication for more details.

David Mercier, Benjamin Quost, Thierry Denœux. Refined modeling of sensor reliability in the belief function framework using contextual discounting. Information Fusion, Volume 9, Issue 2, 2008, Pages 246-258,

Example:

//Contextual discounting  
    double[] m = { 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0 };
    double[] d = { 0.4, 0.6, 0.0 };
    double[] result = new ContextualDiscounting().Discount(m, d);
// result = {0.0, 0.2, 0.0, 0.3, 0.12, 0.08, 0.18, 0.12}

BBA from singletons

In the following publication is explained how to retrieve BBA from singletons whose values correspond to likelihoods obtained from probability density functions.

François Delmotte and Philippe Smets. 2004. Target identification based onthe transferable belief model interpretation of Dempster-Shafer model. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans34, 4(2004), 457–471

Example:

    double[] likelihoods = { 0.053, 0.109 };
    double[] q = HelperMethods.Instance.GetQFromSingletons(likelihoods);
// q = {1.0, 0.053, 0.109, 0.005}
    

In the following publication is explained how to retrieve BBA from singletons whose values correspond to possibilities obtained from possibility distributions.

Didier Dubois, Henri Prade, and Philippe Smets. 2001. New semantics for quantitative possibility theory. In European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Springer, 410–421

Example:

    double[] possibilities = { 0.4, 0.4 };
    double[] pl = HelperMethods.Instance.GetPlFromSingletons(possibilities);
// pl = {0.0, 0.4, 0.4, 0.4}