Abstract
In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal efficiently with both precise and imprecise quantitative and qualitative beliefs, which extends the scope of this theory.
Highlights
Qualitative methods for reasoning under uncertainty have gained more and more attentions by Information Fusion community, especially by the researchers and system designers working in the development of modern multi-source systems for information retrieval, fusion and management in defense, in robotics and so on
Some research works on quantitative imprecise belief structures have been done at the end of nineties by Denœux who proposed a representation model in Dempster-Shafer Theory (DST) framework for dealing with imprecise belief and plausibility functions, imprecise pignistic probabilities together with the extension of Dempster’s rule [1] for combining imprecise belief masses
When Shafer’s model holds, instead of distributing the total conflicting mass onto elements of 2 proportionally with respect to their masses resulted after applying the conjunctive rule as within Demspter’s rule (DS) through the normalization step [20], or transferring the partial conflicts onto partial uncertainties as within DSmH rule [21], we propose to use the Proportional Conflict Redistribution rule no.5 (PCR5) [22, 23] which transfers the partial conflicting masses proportionally to non-empty sets involved in the model according to all integrity constraints
Summary
Qualitative methods for reasoning under uncertainty have gained more and more attentions by Information Fusion community, especially by the researchers and system designers working in the development of modern multi-source systems for information retrieval, fusion and management in defense, in robotics and so on. The goal of this paper is to propose a mathematical model of imprecise qualitative belief structures for solving fusion problems for decision-making support. Some research works on quantitative imprecise (quantitative) belief structures have been done at the end of nineties by Denœux who proposed a representation model in DST framework for dealing with imprecise belief and plausibility functions, imprecise pignistic probabilities together with the extension of Dempster’s rule [1] for combining imprecise belief masses. We introduce new operators based on it for combining imprecise qualitative belief masses, in order to solve fusion problems for decision-making support.
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