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

Alexander Dukhovny

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arXiv · 2510.04314

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

Alexander Dukhovny

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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.

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Alexander Dukhovny. 2025-10-05. Relative Divergence and Maximum Relative Divergence Principle for Grading Functions on Partially Ordered Sets. https://arxiv.org/abs/2510.04314

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