# Enrichment Of Qualitative Beliefs For Reasoning Under Uncertainty

Xinde Li and Xinhan Huang Int. Cont. and Robotics Lab., Dept. of Control Science and Eng.

Huazhong Univ of Sci. and Tech.

Wuhan 430074, China xdl825@163.com Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, U.S.A.

smarand@unm.edu Jean Dezert ONERA
29 Av. de la Division Leclerc 92320 Chˆatillon, France.

Jean.Dezert@onera.fr 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, ∞), 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.

Keywords: **Information fusion, Qualitative beliefs, DSmT, DST.**

## 1 Introduction

Qualitative methods for reasoning under uncertainty have gained more and more attention by Information Fusion community, especially by the researchers and system designers working in the development of modern multi-source systems for defense, robotics and so on. This is because traditional methods based only on quantitative representation and analysis are not able to completely satisfy adequately the need of the development of science and technology integrating at higher fusion levels human beliefs and reports in complex systems. Therefore qualitative knowledge representation becomes more and more **important and necessary in next generations**
of (semi) intelligent automatic and autonomous systems.

For example, Wagner et al. [16] consider that although recent robots have powerful sensors and actuators, their abilities to show intelligent behavior is often limited because of lacking of appropriate spatial representation. Ranganathan et al. [11] describe a navigation system for a mobile robot which must execute motions in a building, the environment is represented by a topological model based on a Generalized Voronoi Graph (GVG) and by a set of visual landmarks. A qualitative self-localization method for indoor environment using a belt of ultrasonic sensors and a camera is proposed. Moratz et al. [6] point **out that qualitative spatial reasoning (QSR)** abstracts metrical details of the physical world, of which two main directions are topological reasoning about regions and reasoning about orientations of point configurations. So, because concrete problems need a combination of qualitative knowledge of orientation and qualitative knowledge **of distance, they present a calculus based**
on ternary relations where they introduce a qualitative distance measurement based on two of the three points.