Fuzzifying the Constraint Hierarchies Framework

R. W. L. Kam, Jimmy Ho-Man Lee

Abstract: The Constraint Hierarchy (CH) framework is used to tackle multiple criteria selection (MCS), consisting of a set of candidates and a set of, possibly competing, criteria for selecting the ”best“ candidate(s). In this paper, we identify aspects of the CH framework for further enancement so as to model and solve MCS problems more accurately. We propose the Fuzzy Constraint Hierarchies framework, which allows constraints to belong to, possibly, more than one level in a constraint hierarchy to a varying degree. We also propose to replace the standard equality relation = used in valuation comparators of the CH framework by the α-approximate equality relation =a(α) for providing more flexible control over the handling of valuations with close error values. These proposals result in three new classes of valuation comparators. Formal properties of the new comparators are given, wherever possible.