A New Evidential Reasoning Rule Considering Interval Uncertainty and Perturbation

Area of Science:

• Decision Sciences
• Artificial Intelligence
• Mathematical Modeling

Background:

• The Evidential Reasoning (ER) rule is a key method in Multiple Attribute Decision Making (MADM), offering transparency via belief structures.
• ER rule's limitations exist in effectively handling interval uncertainty, a common issue in real-world decision problems.

Purpose of the Study:

• To introduce a novel Interval Evidential Reasoning (IER) rule designed to address interval uncertainty in MADM.
• To analyze the robustness of the IER rule against perturbations in belief structures.
• To develop a method for quantifying the IER rule's reliability under uncertain conditions.

Main Methods:

• Proposed a new Interval Evidential Reasoning (IER) rule incorporating interval grades within a new frame of discernment (FoD) to model local ignorance.
• Conducted perturbation analysis (PA) by introducing perturbations to the belief structure to assess the IER rule's stability.
• Established an optimization model to determine the perturbation threshold, measuring inference result effectiveness under perturbation.

Main Results:

• The IER rule was proven to be a generalization of the standard ER rule.
• Perturbation analysis demonstrated the IER rule's behavior and limitations under varying degrees of uncertainty.
• The optimization model effectively estimated perturbation thresholds, providing a quantitative measure of reliability.

Conclusions:

• The proposed IER rule offers an improved approach for MADM problems involving interval uncertainty.
• Perturbation analysis and the developed threshold model provide valuable insights into the IER rule's practical applicability and robustness.
• The IER rule demonstrates effectiveness across various decision-making scenarios, as validated by numerical examples and a case study.