On the structuring of systems with fuzzy relations

Interpretive structural modeling for binary relations and fuzzy structural modeling for fuzzy relations restrict the relation defined on the system being modeled to be either transitive or fuzzy semitransitive. Also, no cycles are allowed in the formal sense. In this paper, we present a new generalized fuzzy structural modeling (GFSM) methodology which does not impose any such restriction on the relation defined on the system while allowing the inclusion of cycles of any order. Algorithms are presented for deriving a minimum-edge connection matrix, automatic detection of hierarchies and cycle condensation. Examples are presented to demonstrate the working of the GFSM algorithms.