Encoding fuzzy possibilistic diagnostics as a constrained optimization problem

This paper discusses a knowledge-base encoding methodology for diagnostic tasks, transforming such knowledge into constrained optimization problems. The methodology is based on a reinterpretation of the consistent causal reasoning paradigm [D. Dubois, H. Prade, Fuzzy relation equations and causal reasoning, Fuzzy Sets and Systems 45 (2) (1995) 119–134] as an equivalent problem of feasibility subject to equality and inequality constraints (in the binary case). Then, it is extended to the fuzzy case. Preferences under uncertain knowledge are incorporated by transforming the feasibility problem into an optimization one, which may be interpreted in possibilistic terms. The problem is solved by efficient, widely-known, linear and quadratic programming tools, which are able to cope with large-scale problems. Examples illustrating some of the concepts and possibilities of the proposed procedure, as well as a summary comparison with other approaches are also discussed.