On the structuring of systems with fuzzy relations.

Area of Science:

• Systems Engineering
• Fuzzy Logic
• Operations Research

Background:

• Traditional interpretive and fuzzy structural modeling methods impose constraints on system relations, such as transitivity or fuzzy semitransitivity.
• These methods also disallow cycles, limiting their applicability to complex systems with inherent feedback loops.

Purpose of the Study:

• To present a novel generalized fuzzy structural modeling (GFSM) methodology.
• To overcome the limitations of existing structural modeling techniques by removing restrictions on relation properties and allowing cycles.

Main Methods:

• Development of the generalized fuzzy structural modeling (GFSM) methodology.
• Algorithms for deriving a minimum-edge connection matrix.
• Algorithms for automatic detection of hierarchies.
• Algorithms for cycle condensation.

Main Results:

• The GFSM methodology successfully models systems without requiring transitive or fuzzy semitransitive relations.
• The approach accommodates systems with cycles of any order.
• Algorithms for matrix derivation, hierarchy detection, and cycle condensation are demonstrated.

Conclusions:

• GFSM offers a more flexible and comprehensive approach to structural modeling compared to traditional methods.
• The methodology is applicable to a wider range of complex systems, including those with cyclical relationships.
• The presented algorithms provide practical tools for analyzing complex system structures.