The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N , K, T , and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows o...

We present a deterministic algorithm that counts the number of satisfying assignments for any de Morgan formula F of size at most n3−16ε in time 2n−n ε · poly(n), for any small constant ε > 0. We do this by derandomizing the randomized algorithm mentioned by Komargodski et al. (FOCS, 2013) and Chen et al. (CCC, 2014). Our result uses the tight “shrinkage in expectation” result of de Morgan form...

—In this paper, we examine and compare de Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms in fuzzy settings. This generalizes papers of Turksen on the subject of Boolean-normal forms.

1 School of Mathematical Sciences, Queensland University of Technology, P.O. Box 2434, Brisbane, QLD 4001, Australia 2 Department of Bioengineering, University of Illinois, 851 South Morgan Street, Chicago, IL 60607, USA 3Department of Mathematics, Shanghai University, Shanghai 200444, China 4Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA 5Depar...