Random Permutation Set Reasoning

Area of Science:

• Artificial Intelligence
• Pattern Recognition
• Uncertainty Reasoning

Background:

• Processing uncertain data is crucial for AI pattern recognition systems.
• Evidence theory is a key approach for uncertainty reasoning.
• Random Permutation Set (RPS) theory, an extension of evidence theory, offers orderable reasoning but lacks methods for generating permutation mass functions (PMF) and determining fusion order for permutation orthogonal sums (POS).

Purpose of the Study:

• To address limitations in RPS theory by proposing a novel reasoning model.
• To develop methods for generating PMF element order and determining POS fusion order.
• To enhance uncertainty reasoning in AI pattern recognition.

Main Methods:

• Introduction of Random Permutation Set Reasoning (RPSR) model.
• Development of RPS Generation Method (RPSGM) using Gaussian discriminant model and weight analysis.
• Implementation of RPSR rule of combination incorporating POS with reliability vectors.
• Utilization of Ordered Probability Transformation (OPT) for converting RPS to probability distributions.

Main Results:

• RPSGM successfully constructs RPS, addressing PMF generation.
• The RPSR rule enables reliable fusion of RPS sources in a determined order.
• OPT effectively transforms RPS into usable probability distributions for decision-making.
• Numerical examples validated the RPSR model's functionality.
• An RPSR-based classification algorithm (RPSRCA) demonstrated efficiency and stability.

Conclusions:

• The proposed RPSR model effectively overcomes limitations in existing RPS theory.
• RPSR provides robust methods for handling uncertainty in AI pattern recognition.
• RPSRCA shows competitive performance compared to existing classification methods, highlighting the practical utility of RPSR.