Resumen de Information theory and consensual processes in qualitative reasoning
This dissertation presents an approach to information theory and consensual processes within the framework of qualitative reasoning, Three are the main contributions of this dissertation. The first part contributes to mathematical formalizations of qualitative reasoning. This dissertation introduces a new generalized qualitative absolute orders-of-magnitude model with an algebraic structure that ensures initial conditions to adapt the measure theory to a qualitative environment. The algebraic structure induced in the set of qualitative descriptions in group decision-making and evaluation processes is studied. The results demonstrate that it is a weak partial lattice structure that in some conditions takes the form of a distributive lattice. In this context a distance is introduced conducting to a metric lattice structure.
This theory provides the appropriate framework to introduce the concept of entropy and, consequently, to develop an information theory. The second contribution of this dissertation is the study of entropy in absolute orders-of-magnitude qualitative spaces together with the structures and concepts necessary to introduce it and its application to assess consensus in group decision-making. The concept of entropy of a qualitatively described system is defined and the properties of this function are studied in detail. This enables us, on the one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. The new approach to study consensual processes presented is capable of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus regarding the group decision, an automatic process assesses the effort required to achieve said consensus.
The third contribution is framed in automated model construction and qualitative machine learning. It puts forward a new strategy for recommendation systems and develops a new recommender system that takes into account the lack of precision of users' opinions. The proposed system, different from existing recommender systems, is based on the concept of entropy and allows the recommendation to be derived from the nearest neighbour within a group that is in consensus. The previous search of groups being in consensus with the user makes it easier to and with lower cost of calculating a minimum distance. In addition, this system addresses the new item problem and is appropriate for recommending new items to customers.
