Abstract
In this paper, we generalize the basic notions and results of Dempster-Shafer theory from predicates to formal concepts. Results include the representation of conceptual belief functions as inner measures of suitable probability functions, and a Dempster-Shafer rule of combination on belief functions on formal concepts.
Highlights
Dempster-Shafer theory Dempster-Shafer theory [5,18] is a formal framework for decision-making under uncertainty in situations in which some predicates cannot be assigned subjective probabilities
The core proposal of Dempster-Shafer theory is that, in such cases, the missing value can be replaced by a range of values, the lower and upper bounds of which are assigned by belief and plausibility functions
The present paper is a case in point: building on [1, Section 7.3], we propose a generalization of Dempster-Shafer theory to formal concepts
Summary
Dempster-Shafer theory Dempster-Shafer theory [5,18] is a formal framework for decision-making under uncertainty in situations in which some predicates cannot be assigned subjective probabilities. We provide both a purely algebraic proof and a frame theoretic proof of that result. The former highlights why the construction provides belief and plausibility functions, while the latter allows the reader to understand the structure of conceptual probability space on which the inner and outer measures are interpreted. To answer the question: to which category does an unknown object belong?
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