Interval-based uncertain reasoning

This thesis examines three interval based uncertain reasoning approaches: reasoning under interval constraints, reasoning using necessity and possibility functions, and reasoning with rough set theory. In all these approaches, intervals are used to characterize the uncertainty involved in a reasoning process when the available information is insufficient for single-valued truth evaluation functions. Approaches using interval constraints can be applied to both interval fuzzy sets and interval probabilities. The notion of interval triangular norms, or interval t-norms for short, is introduced and studied in both numeric and non-numeric settings. Algorithms for computing interval t-norms are proposed. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are studied. Inference rules for reasoning under interval constraints are investigated. In the second approach, a pair of necessity and possibility functions is used to bound the fuzzy truth values of propositions. Inference in this case is to narrow the gap between the pair of the functions. Inference rules are derived from the properties of necessity and possibility functions. The theory of rough sets is used to approximate truth values of propositions and to explore modal structures in many-valued logic. It offers an uncertain reasoning method complementary to the other two

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio