Applying models of imprecise probabilities in the mathematical theory of criteria importance
We show that if preferences can be defined with an additive utility function then decision making models based on the theory of criteria importance can be defined with imprecise probabilities. With this idea, we analyze new approaches to decision making in the theory of criteria importance.
The motion detection in video is considered. We break non-binary motion mask on blocks and calculate a certain statistics for each block. Then we use prior information about statistics distribution to classify blocks on background and foreground. The estimation framework for classification confidence is presented.
In the paper we continue investigations started in the paper presented at ISIPTA’15, where the notions of lower and upper generalized credal sets has been introduced. Generalized credal sets are models of imprecise probabilities, where it is possible to describe contradiction in information, when the avoiding sure loss condition is not satisfied. The paper contains the basic principles of approximate reasoning: models of uncertainty based on upper previsions and generalized credal sets, natural extension, and coherence principles.
In the paper we consider the generalization of the conjunctive rule in the theory of imprecise probabilities. Let us remind that the conjunction rule, produced on credal sets,gives their intersection and it is not defined if this intersection is empty. In the last case the sources of information are called contradictory1. Meanwhile, in the Dempster-Shafer theory it is possible to use the conjunctive rule for contradictory sources of information having as a result a nonnormalized belief function that can be greater than zero at empty set. In the paper we try to exploit this idea and introduce into consideration so called generalized credal sets allowing to model imprecision (non-specificity), conflict, and contradiction in information. Based on generalized credal sets the conjunctive rule is well defined for contradictory sources of information and it can be conceived as the generalization of the conjunctive rule for belief functions. We also show how generalized credal sets can be used for modeling information when the avoiding sure loss condition is not satisfied, and consider coherence conditions and natural extension based on generalized credal sets.
To model conflict, non-specificity and contradiction in information, upper and lower generalized credal sets are introduced. Any upper generalized credal set is a convex subset of plausibility measures interpreted as lower probabilities whose bodies of evidence consist of singletons and a certain event. Analogously, contradiction is modelled in the theory of evidence by a belief function that is greater than zero at empty set. Based on generalized credal sets, we extend the conjunctive rule for contradictory sources of information, introduce constructions like natural extension in the theory of imprecise probabilities and show that the model of generalized credal sets coincides with the model of imprecise probabilities if the profile of a generalized credal set consists of probability measures. We give ways how the introduced model can be applied to decision problems.