This study proposes the Interval-Confidence Risk Theory (ICRT) as a new theoretical foundation for quantitative risk assessment in judgment-driven and data-limited environments. The purpose is to address persistent limitations of existing probabilistic, fuzzy, evidential, and hierarchy-based approaches, particularly their inability to explicitly distinguish uncertainty in risk magnitude from uncertainty in evidence reliability.
The study develops a formal measurement theory in which risk is represented as an interval–confidence pair within a bounded 0–100 numerical domain. Axioms governing boundedness, monotonicity, continuity, confidence propagation and interpretability are defined. Operator-based mechanisms for dependency, accumulation, mitigation and projection are introduced to aggregate multidimensional risk attributes. The proposed theory is operationalised through a structured eight-step procedure and demonstrated using a worked example to illustrate practical applicability, interpretability, and decision-oriented usability across judgment-driven risk contexts.
The paper establishes that risk can be quantified as a dual-layer construct combining interval-based uncertainty with explicit confidence representation, enabling the separation of value variability from evidence reliability. The proposed theory demonstrates that risk aggregation, mitigation and projection can be performed within a bounded and closed numerical domain while preserving uncertainty throughout the analytical process.
This study provides a methodological contribution by introducing a structured measurement framework for risk assessment that integrates interval uncertainty and confidence propagation within a unified structure. The interval-confidence representation extends existing uncertainty modeling approaches by enabling transparent propagation of confidence during risk quantification. As a result, ICRT offers a structured methodological foundation for developing new analytical tools and decision-support models in judgment-driven risk assessment contexts.
This study provides a methodological contribution by introducing a formal measurement framework for risk assessment that integrates interval uncertainty and confidence propagation within a unified structure. The proposed axiomatic formulation and operator-based aggregation mechanisms offer a systematic method for modeling multidimensional risk attributes while preserving both value variability and evidential reliability. The interval-confidence representation extends existing uncertainty modeling approaches by enabling transparent propagation of confidence during aggregation and mitigation. As a result, ICRT offers a structured methodological foundation for developing new analytical tools and decision-support models in judgment-driven risk assessment contexts.
This study introduces a novel measurement-oriented risk theory that explicitly integrates interval uncertainty and confidence within a unified and bounded numerical framework. Unlike existing methods, ICRT formally separates value uncertainty from evidence reliability and integrates confidence propagation directly into risk aggregation. The theory bridges decision science, uncertainty modeling and multi-criteria analysis, offering original conceptual, mathematical and practical contributions to quantitative risk assessment in judgment-driven contexts.
