Conditional Independence in Possibility Theory

TL;DR

This paper explores possibilistic conditional independence, defining it similarly to probability theory, analyzing its properties, and examining how different conjunctions affect the conditional measure of possibility.

Contribution

It introduces a possibilistic conditional independence definition, investigates its properties, and analyzes the impact of various conjunctions on the conditional measure.

Findings

Links between independence and non-interactivity are established.

Properties of possibilistic independence are characterized.

The influence of different conjunctions on conditional measures is analyzed.

Abstract

Possibilistic conditional independence is investigated: we propose a definition of this notion similar to the one used in probability theory. The links between independence and non-interactivity are investigated, and properties of these relations are given. The influence of the conjunction used to define a conditional measure of possibility is also highlighted: we examine three types of conjunctions: Lukasiewicz - like T-norms, product-like T-norms and the minimum operator.