D-S Evidence Theory and D-S Evidence Combination Rule with MATLAB Implementation

D-S Evidence Theory (Dempster-Shafer Theory) is a mathematical framework for handling uncertainty and incomplete information reasoning, widely applied in decision analysis, sensor fusion, fault diagnosis, and other domains. By introducing belief functions and plausibility functions, this theory provides a flexible approach to represent and combine evidence from diverse sources.

One of the core components of D-S Evidence Theory is the evidence combination rule (Dempster's Rule of Combination), which merges belief measures from multiple evidence sources. This rule first calculates the Basic Probability Assignment (BPA) for each evidence source, then normalizes conflicting evidence through a conflict coefficient calculation, ultimately producing a combined belief measure. This process effectively handles information uncertainty and plays a vital role in scenarios like multi-sensor data fusion.

In MATLAB implementation, we can encapsulate the D-S evidence combination rule into a reusable function. The function would accept multiple BPAs as input parameters, typically structured as a matrix or cell array where each row represents an evidence source's probability assignments. The output would be a synthesized belief distribution, possibly including conflict coefficients and normalization factors. Key implementation steps involve: 1) Calculating the orthogonal sum of mass functions 2) Handling conflicts using Dempster's normalization 3) Returning combined belief intervals. This modular design allows easy integration into existing systems for applications like multi-sensor information fusion and risk assessment.

Furthermore, the MATLAB function can be enhanced with additional features such as configurable confidence thresholds, conflict coefficient monitoring, and support for different combination strategies (e.g., Yager's or Dubois-Prade's rules). Through parameterized design, users can adjust evidence weights and combination parameters to accommodate various application requirements. The function might include input validation, error handling for incompatible frames of discernment, and visualization options for result interpretation.

In summary, D-S Evidence Theory and its combination rule hold significant value in uncertainty reasoning, while MATLAB implementation provides an efficient, customizable platform for practical applications. The code structure typically involves main combination logic, conflict resolution algorithms, and result normalization procedures, making complex uncertainty reasoning accessible to researchers and engineers.