Positive and Negative Explanations of Uncertain Reasoning in the Framework of Possibility Theory

TL;DR

This paper develops explanation methods for rule-based expert systems handling uncertain knowledge within possibility theory, focusing on positive and negative explanations of how and why certain possibility distributions are derived.

Contribution

It introduces a formal approach using max-min algebra to generate explanations for uncertain reasoning in possibility theory, including both positive and negative aspects.

Findings

Explanation methods for possibility distributions are formalized.

The approach covers both certain and uncertain information.

It enhances interpretability of expert systems managing imprecise data.

Abstract

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the available information concerning the value of a logical or numerical variable is represented by a possibility distribution which restricts its more or less possible values. We first discuss different kinds of queries asking for explanations before focusing on the two following types : i) how, a particular possibility distribution is obtained (emphasizing the main reasons only) ; ii) why in a computed possibility distribution, a particular value has received a possibility degree which is so high, so low or so contrary to the expectation. The approach is based on the exploitation of equations in max-min algebra. This formalism includes the limit case of certain and precise information.