Maximum Relative Divergence Principle for Grading Functions on Power Sets

TL;DR

This paper extends the concept of Relative Divergence and Shannon Entropy to grading functions on power sets, introducing the Maximum Relative Divergence Principle to identify the most reasonable grading functions for applications in Operations Research.

Contribution

It generalizes divergence and entropy concepts to power sets and introduces the Maximum Relative Divergence Principle as a new method for selecting optimal grading functions.

Findings

Extended Relative Divergence to power sets.

Extended Shannon Entropy to normalized grading functions.

Introduced Maximum Relative Divergence Principle for applications.

Abstract

The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets. Maximum Relative Divergence Principle is introduced as a generalization of the Maximum Entropy Principle as a tool for determining the "most reasonable" grading function and used in some Operations Research applications where that function is supposed to be "element-additive" or "cardinality-dependent" under application-specific linear constraints.