Halaby, M. E., "Solving MaxSAT by Successive Calls to a SAT Solver", In Proceedings of SAI Intelligent Systems Conference (IntelliSys 2016). Springer International Publishing. Pages: 428-452. DOI: https://doi.org/10.1007/978-3-319-56994-9_31. ISBN: 978-3-319-56994-9, London, UK, 2016.
Halaby, M. E., and A. Abdalla, "Fuzzy Maximum Satisfiability", 10th International Conference on Informatics and Systems (INFOS 2016), ACM ICPS, Giza, Egypt, 2016. Abstract

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.

Halaby, M. E., "On the Computational Complexity of MaxSAT", ECCC (Electronic Colloquium on Computational Complexity), 2016. on_the_computational_complexity_of_maxsat.pdf

Discrete Mathematics