Tesis doctoral de Enric Hernandez Jimenez
The concept of equality is a fundamental notion in any theory since it is essential to the ability of discerning the objects to whom it concerns, ability which in turn is a requirement for any classification mechanism that might be defined. When all the properties involved are entirely precise, what we obtain is the classical equality, where two individuals are considered equal if and only if they share the same set of properties. What happens, however, when imprecision arises as in the case of properties which are fulfilled only up to a degree? Then, because certain individuals will be more similar than others, the need for a gradual notion of equality arises. These considerations show that certain contexts that are pervaded with uncertainty require a more flexible concept of equality that goes beyond the rigidity of the classic concept of equality. T-indistinguishability operators seem to be good candidates for this more flexible and general version of the concept of equality that we are searching for. On the other hand, dempster-shafer theory of evidence, as a framework for representing and managing general evidences, implicitly conveys the notion of indistinguishability between the elements of the domain of discourse based on their relative compatibility with the evidence at hand. In chapter two we are concerned with providing definitions for the t-indistinguishability operator associated to a given body of evidence. In chapter three, after providing a comprehensive summary of the state of the art on measures of uncertainty, we tackle the problem of computing entropy when an indistinguishability relation has been defined over the elements of the domain. Entropy should then be measured not according to the occurrence of different events, but according to the variability perceived by an observer equipped with indistinguishability abilities as defined by the indistinguishability relation considered. This idea naturally leads to the introduction of the concept of o
Datos académicos de la tesis doctoral «Uncertainty and indistinguishability. application to modelling with words«
- Título de la tesis: Uncertainty and indistinguishability. application to modelling with words
- Autor: Enric Hernandez Jimenez
- Universidad: Politécnica de catalunya
- Fecha de lectura de la tesis: 12/01/2007
Dirección y tribunal
- Director de la tesis
- Jorge Recasens Ferres
- Tribunal
- Presidente del tribunal: joan Jacas moral
- jonathan Lawry (vocal)
- lluís Godó lacasa (vocal)
- adolfo Rodríguez de soto (vocal)