Author_Institution :
Human-Machines-Interaction (HMI) Lab., Technol. Educ. Instn. of Kavala, Agios Loukas, Greece
Abstract :
This work introduces the Boolean (quotient) lattice (QI, ⊆), an element of whom is the union of countable (closed) intervals on the real line. It follows that (QI, ∪, ∩, ´) is a lattice implication algebra (LIA), the latter is an established framework for reasoning under uncertainty. It is illustrated in (QI, ∪, ∩, ´) how fuzzy lattice reasoning (FLR) techniques, for tunable decision-making, can be extended to lattice-valued logic. Potential practical applications are described.
Keywords :
Boolean functions; decision making; fuzzy reasoning; uncertainty handling; Boolean lattice; FLR extension; FLR technique; LIA; closed intervals; countable intervals; fuzzy lattice reasoning; lattice implication algebra; lattice-valued logic; quotient lattice; reasoning under uncertainty; tunable decision-making; Algebra; Cognition; Cost accounting; Decision making; Instruments; Lattices; Uncertainty; Fuzzy lattice reasoning; Inclusion measure; Lattice-valued logic; The lattice computing paradigm; Tunable decision-making;
