A point inside the triangle represents a triple. The b,d,u-axes run from one edge to the opposite vertex indicated by the Belief, Disbelief or Uncertainty label. For example, a strong positive opinion is represented by a point towards the bottom right Belief vertex. The base rate, also called the prior probability, is shown as a red pointer along the base line, and the projected probability, , is formed by projecting the opinion onto the base, parallel to the base rate projector line. Opinions about three values/propositions X, Y and Z are visualized on the triangle to the left, and their equivalent Beta PDFs (Probability Density Functions) are visualized on the plots to the right. The numerical values and verbal qualitative descriptions of each opinion are also shown. The Beta PDF is normally denoted as where and are its two strength parameters. The Beta PDF of a binomial opinion is the function where is the non-informative prior weight, also called a unit of evidence, normally set to . Multinomial opinions Let be a state variable which can take state values . A multinomial opinion over is the composite tuple , where is a belief mass distribution over the possible state values of , is the uncertainty mass, and is the prior (base rate) probability distribution over the possible state values of . These parameters satisfy and as well as . Trinomial opinions can be simply visualised as points inside a tetrahedron, but opinions with dimensions larger than trinomial do not lend themselves to simple visualisation. Dirichlet PDFs are normally denoted as where is a probability distribution over the state values of , and are the strength parameters. The Dirichlet PDF of a multinomial opinion is the function where the strength parameters are given by , where is the non-informative prior weight, also called a unit of evidence, normally set to . Operators Most operators in the table below are generalisations of binary logic and probability operators. For example addition is simply a generalisation of addition of probabilities. Some operators are only meaningful for combining binomial opinions, and some also apply to multinomial opinion. Most operators are binary, but complement is unary, and abduction is ternary. See the referenced publications for mathematical details of each operator. Transitive source combination can be denoted in a compact or expanded form. For example, the transitive trust path from analyst/source via source to the variable can