  This article discusses the theory, model, implementation and performance of a
combinatorial fuzzy-binary and-or (FBAR) algorithm for lossless data
compression (LDC) and decompression (LDD) on 8-bit characters. A combinatorial
pairwise flags is utilized as new zero/nonzero, impure/pure bit-pair operators,
where their combination forms a 4D hypercube to compress a sequence of bytes.
The compressed sequence is stored in a grid file of constant size.
Decompression is by using a fixed size translation table (TT) to access the
grid file during I/O data conversions. Compared to other LDC algorithms,
double-efficient (DE) entropies denoting 50% compressions with reasonable
bitrates were observed. Double-extending the usage of the TT component in code,
exhibits a Universal Predictability via its negative growth of entropy for LDCs
> 87.5% compression, quite significant for scaling databases and network
communications. This algorithm is novel in encryption, binary, fuzzy and
information-theoretic methods such as probability. Therefore, information
theorists, computer scientists and engineers may find the algorithm useful for
its logic and applications.
