On revising fuzzy belief bases

TL;DR

This paper extends the concept of belief base revision to fuzzy logic, allowing formulas with varying truth degrees, and introduces an axiomatized partial meet fuzzy revision operation applicable in diverse fuzzy inference frameworks.

Contribution

It develops a general framework for revising fuzzy belief bases, extending partial meet revision from crisp to fuzzy contexts with formal axiomatization.

Findings

Introduces a formal partial meet fuzzy revision operation.

Applies the framework to various fuzzy inference systems.

Provides axiomatic foundations for fuzzy belief revision.

Abstract

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture a variety of types of inference under uncertainty, such as truth-functional fuzzy logics and certain types of probabilistic inference, we show how the idea of rational change from 'crisp' base revision, as embodied by the idea of partial meet revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy revision and illustrate how the operation works in several important special instances of the framework.