Inheritance and recognition in uncertain and fuzzy object-oriented models

The paper proposes probabilistic default reasoning as a suitable approach to inheritance and recognition in uncertain and fuzzy object-oriented models. Firstly, we introduce an uncertain and fuzzy object-oriented model where a class property (i.e., an attribute or a method) can contain fuzzy sets interpreted as families of probability distributions, and uncertain class membership and property applicability are measured by lower and upper bounds on probability. Each uncertainty applicable property is interpreted as a default probabilistic logic rule, which is defeasible. In order to reduce the computational complexity of general probabilistic default reasoning, we propose to use R. Jeffrey's (1965) rule for a weaker notion of consistency and for local inference, then apply them to uncertain inheritance of properties. Using the same approach but with inverse Jeffrey's rule, uncertain recognition as probabilistic default reasoning is also presented. The approach is illustrated by an example in Fril++, the uncertain and fuzzy object-oriented logic programming language that we have been developing.