Possibilistic Evaluation of Sets

Abstract

In the past decades, the theory of possibility has been developed as a theory of uncertainty that is compatible with the theory of probability. Whereas probability theory tries to quantify uncertainty that is caused by variability (or equivalently randomness), possibility theory tries to quantify uncertainty that is caused by incomplete information. A specific case of incomplete information is that of ill-known sets, which is of particular interest in the study of temporal databases. However, the construction of possibility distributions in the case of ill-known sets is known to be overly complex. This paper contributes to the study of ill-known sets by investigating the inference of uncertainty when constraints are specified over ill-known values. More specific, in this paper it is investigated how the knowledge about constraint satisfaction can be inferred if the constraints themselves are defined by means of ill-known values. It is shown how such reasoning can contribute to the study of (fuzzy) temporal databases.

Combining quantifications for flexible query result ranking

“…Often, a set of data exists, each of which could be the intended datum. In those cases, it is said that the datum is subject to uncertainty [1], [2], [5], [8], [12], [21], [24]- [27]. Usually, for a datum subject to uncertainty, an attempt is made to model the available knowledge about the intended datum, by assigning each of the data which could be the intended datum a degree of confidence an agent has that the corresponding datum is the intended datum.…”

“…Depending on the source of the circumstances of the uncertainty, such confidence can take different forms, where different forms have different interpretations and different handling rules. When the source is variability, confidence usually takes the form of chance and probability theory is used [1], [12], [26], [27]. When the source is a (partial) lack of knowledge, confidence usually takes the form of possibility and possibility theory is used [1], [8], [12], [21], [24], [25].…”

“…For example, consider table I, which is the visualization of an example relational database relation containing data representing 3 properties of each of 5 rental cars. For every such car, data representing a unique ID number, the color of the car and an ill-known time interval [1]- [3], [12]- [15] determining when the car might be available for rent, are stored. The first row in the table contains these properties' (or in the context of databases: attributes') names, every other row visualizes the values representing these properties for one car.…”

“…The interpretation is: an exact time interval during which a car is available, is intended, but due to a (partial) lack of knowledge about the circumstances determining this interval, it is uncertain exactly which interval is intended. In order to model confidence about which interval is intended, every existing time interval is given a possibility degree, which is interpreted as the degree of how plausible it is, given all available knowledge, that the corresponding time interval is the intended interval [1]- [3], [12]- [15].…”

Twodimensional Visualization of Discrete Time Domain Intervals Subject to Uncertainty

“…Among others, uncertainty about the outcome of an experiment can be caused by a (partial) lack of knowledge: it could be known that only one outcome may occur, but as the experiment is not perfectly and comprehensively known or controlled, the outcome of the experiment may be unknown and thus uncertain. Confidence in the context of uncertainty caused by a (partial) lack of knowledge is modeled using possibility theory, where possibility is interpreted as plausibility, given all available knowledge (Bronselaer et al, 2013). Based on prior experiences, it is the belief of the authors that uncertainty concerning time is usually caused by a (partial) lack of knowledge.…”