Enrichment of Qualitative Beliefs for Reasoning under Uncertainty

TL;DR

This paper introduces enriched qualitative belief functions with new operators for reasoning under uncertainty, extending existing qualitative operators to incorporate quantitative and qualitative enrichments, facilitating natural language information fusion.

Contribution

It proposes $qe$-operators for enriched belief functions, extending qualitative operators in DSmT to handle both quantitative and qualitative enrichments of linguistic labels.

Findings

Operators enable fusion of enriched belief assignments.

Quantitative enrichment uses numerical degrees, qualitative uses ordered linguistic sets.

Examples demonstrate practical application of the proposed operators.

Abstract

This paper deals with enriched qualitative belief functions for reasoning under uncertainty and for combining information expressed in natural language through linguistic labels. In this work, two possible enrichments (quantitative and/or qualitative) of linguistic labels are considered and operators (addition, multiplication, division, etc) for dealing with them are proposed and explained. We denote them $qe$-operators, $qe$ standing for "qualitative-enriched" operators. These operators can be seen as a direct extension of the classical qualitative operators ($q$-operators) proposed recently in the Dezert-Smarandache Theory of plausible and paradoxist reasoning (DSmT). $q$-operators are also justified in details in this paper. The quantitative enrichment of linguistic label is a numerical supporting degree in $[0,\infty)$, while the qualitative enrichment takes its values in a finite ordered set of linguistic values. Quantitative enrichment is less precise than qualitative enrichment, but it is expected more close with what human experts can easily provide when expressing linguistic labels with supporting degrees. Two simple examples are given to show how the fusion of qualitative-enriched belief assignments can be done.