Relative Divergence and Maximum Relative Divergence Principle for Grading Functions on Partially Ordered Sets

Abstract

Relative Divergence (RD) and Maximum Relative Divergence Principle (MRDP) for grading (order-comonotonic) functions (GF) on posets are used as an expression of Insufficient Reason Principle under the given prior information (IRP+). Classic Probability Theory formulas are presented as IRP+ solutions of MRDP problems on conjoined posets. RD definition principles are analyzed in relation to the poset structure. MRDP techniques are presented for standard posets: power sets, direct products of chains, etc. "Population group-testing" and "Single server of multiple queues" applications are stated and analyzed as "IRP+ by MRDP" problems on conjoined base posets.