The fuzzy parametrized model for classifying blocks in the non-binary motion mask
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.
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.
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.
Recently, generalized credal sets have been introduced for modeling contradiction (incoherence) in the information. In previous papers, we did not discuss how such information could be updated if some events occur. In this paper, we show that it can be done by the conjunctive rule based on generalized credal sets.We show that the application of generalized credal sets results in several types of conditioning for imprecise probabilities.
Process mining is a new direction in the field of modeling and analysis of processes, where an important role is played by the use of information from event logs that describe the history of the system behavior. Methods and approaches used in process mining are often based on various heuristics, and experiments with large event logs are crucial for substantiating and comparing developed methods and algorithms. These experiments are very time consuming, so automation of experiments is an important task in the field of process mining. This paper presents the DPMine language developed specifically to describe and carry out process mining experiments. The basic concepts of the DPMine language as well as principles and mechanisms of its extension are described. Ways of integration of the DPMine language as dynamically loaded components into the VTMine modeling tool are considered. A sample experiment of building a fuzzy model of a process from a data log stored in a normalized database is given.