2CoBel

2CoBel is a library for Belief Function Theory (BFT) in 2D (and 1D) continuos spaces. Please cite the referring paper if you use the library in your project:

@inproceedings{pellicano18ijar, author = {Pellican{`o}, Nicola and Le H{'e}garat-Mascle, Sylvie and Aldea, Emanuel }, title = "2CoBel: A scalable belief function representation for 2D discernment frames", journal = "International Journal of Approximate Reasoning", volume = "103", pages = "320 - 342", year = "2018" }

Dependencies

• Python 2.7(for plotting)
• Eigen

The already resolved dependencies are Clipper and a modified version of matplotlib-cpp.

Supported focal elements types

• UnidimensionalFocalElement (see demos/unidimensional_demo.cpp)
• Clipper2DFocalElement (see demos/clipper_demo.cpp)
• EigenMat2DFocalElement
• BoxSet2DFocalElement
• CompositeFocalElement (for cross product spaces)

Example (demos/clipper_demo.cpp)

A discernment frame is built as a rectangular focal element, by specifiying its vertexes.

  std::vector<Geometry::Point2D> dfp;
  dfp.emplace_back(0, 0);
  dfp.emplace_back(100, 0);
  dfp.emplace_back(100, 100);
  dfp.emplace_back(0, 100); //counterclockwise
  Geometry::ClipperPolygon dfpoly(dfp);
  std::unique_ptr<FocalElement> df(new Clipper2DFocalElement(dfpoly));

All the BBAs are built (see the code for reference)

  buildEvidence(*df);

Creation of BBA D as the disjunctive combination between BBAs A and B.

   Evidence evD = evA->disjunctive_rule(*evB);

BBAs C and D.

Discounting of BBA C.

  evC->discount(0.1);

Conjunctive combination of BBA C and D.

  Evidence ev_final = evC->conjunctive_rule(evD);

BetP maximization

   std::unique_ptr<FocalElement> argmaxBetP = ev_final.maxBetP_withMaximalIntersections();