We report a method for counting uncertain data, i.e. observations that cannot be precisely associated to referents. We model data uncertainty through Possibility Theory and we develop the counting method so as to take into account the possibility distributions attached to data. The result is a fuzzy interval on the domain of natural numbers, which can be obtained by two variants of the method: exact counting provides the true fuzzy interval in quadratic time complexity, while approximate counting carries out an estimate of the fuzzy interval in linear time. We give a step-by-step description of the method so that it can be replicated in any programming environment. We also provide a Python implementation and a use case in Bioinformatics. The method usage is the following: • The uncertain data are represented in form of matrix, one row for each observation. Each row is a possibility distribution; • The method variant must be selected. In the case of the approximate variant, the number of α-values of the resulting fuzzy interval must be provided; • For each referent, a fuzzy interval is determined and carried out by the method.

### GrCount: Counting method for uncertain data

#### Abstract

We report a method for counting uncertain data, i.e. observations that cannot be precisely associated to referents. We model data uncertainty through Possibility Theory and we develop the counting method so as to take into account the possibility distributions attached to data. The result is a fuzzy interval on the domain of natural numbers, which can be obtained by two variants of the method: exact counting provides the true fuzzy interval in quadratic time complexity, while approximate counting carries out an estimate of the fuzzy interval in linear time. We give a step-by-step description of the method so that it can be replicated in any programming environment. We also provide a Python implementation and a use case in Bioinformatics. The method usage is the following: • The uncertain data are represented in form of matrix, one row for each observation. Each row is a possibility distribution; • The method variant must be selected. In the case of the approximate variant, the number of α-values of the resulting fuzzy interval must be provided; • For each referent, a fuzzy interval is determined and carried out by the method.
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11586/256327`
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