Fuzzy Maximum Satisfiability
This work addresses optimization problems with vagueness for researchers in logic and AI, but it is incremental as it extends an existing problem to a new logic.
The paper tackles the extension of the Maximum Satisfiability problem to Łukasiewicz logic, proposing three encodings (DLRs, MILP, WCSP) to solve it, with potential applications in optimization involving vagueness.
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to Łukasiewicz logic. The MaxSAT problem for a set of formulae Φ is the problem of finding an assignment to the variables in Φ that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.