Fuzzy information granular structures: A further investigation.

Fuzzy information granular structures, abbreviated as FI granular structures, refers to a mathematical structure in the family of fuzzy information granules (for short, FI granules). Although some excellent research contributions have been made, two important problems still remain to be solved: What are the dependence and independence between FI granular structures? Can we give characteristics of FI granular structures? This paper mainly considers these two problems. The dependence between FI granular structures is first addressed. Then, operators on the fuzzy granular structure base are studied. Next, properties of FI granular structures are given. Finally, algebraic, lattice and map characteristics of FI granular structures are obtained, and invariant characteristics of FI granular structures under homomorphisms based on data compression are provided.