Fuzzy constraint processing
Kouhua Robert Lai · 1992
This thesis presents a computational model for representing and reasoning about imprecise information in a network of constraints. We adopt a possibilitic approach to representing imprecision. As a result, fuzzy logic, which is an extension of classical logic, can be used to provide a conceptual framework for imprecise constraints. A theory of fuzzy constraint processing is then introduced and used as the basis for proving several theorems, including results that involve soundness, incompleteness and uniqueness. To exercise this theory, we implemented a programming language, called Khayyam, for fuzzy constraint processing. In Khayyam, a well-formed constraint is any first-order fuzzy logic sentence (atomic, compound or quantified) about a many-sorted universe of discourse which includes, besides the real numbers $\Re$, arbitrary application-specific sorts. Problem solving in Khayyam is interactive, with user edits of the network being interleaved with constraint refinement by the run-time system. The utility of the system is illustrated by example applications in decision support and engineering design.