A Formal Metric to Measure Inconsistencies in Stakeholder Preferences in Systems Engineering

ABSTRACT Developing complex systems like satellites and aircraft organizations involve numerous decision‐makers across various levels. These stakeholders, internal or external, express preferences traditionally through textual needs statements. Textual needs statements are easy to formulate and use, but offer limited analytical capacity. Alternative approaches based on decision analysis facilitate representing preferences rigorously but prove resource intensive without accuracy guarantees. Recently, researchers have proposed modal preference logic (MPL) to mathematically represent and reason about stakeholder preferences in systems engineering. Past work has demonstrated MPL's promise in identifying preference inconsistencies. This paper builds on that foundation to advance new theory and methods for systematically measuring detected inconsistencies. It introduces the Inconsistency Magnitude (IM), a rigorously developed metric grounded in minimal inconsistent subsets that sensitively quantifies inconsistencies and the spread of inconsistencies. Underpinning this metric, several theorems are presented that prove key properties across syntax variations. The research computationally exemplifies the metric over sample preference bases exhibiting differing complexity levels of inconsistencies.