Fuzzy Lattice Reasoning (FLR) Extensions to Lattice-Valued Logic

Abstract

This work introduces the Boolean (quotient) lattice (Q_I, ⊆), an element of whom is the union of countable (closed) intervals on the real line. It follows that (Q_I, ∪, ∩, ') is a lattice implication algebra (LIA), the latter is an established framework for reasoning under uncertainty. It is illustrated in (Q_I, ∪, ∩, ') how fuzzy lattice reasoning (FLR) techniques, for tunable decision-making, can be extended to lattice-valued logic. Potential practical applications are described.