Fuzzy evidential influence diagram and its evaluation algorithm

摘要

Fuzzy influence diagrams (FIDs) are graphical models that combine qualitative and quantitative analyses to solve decision-making problems though some shortcomings that need to be corrected still remain. One is to guarantee the exactness as node evaluation in high-complexity influence diagrams (IDs) need to be combined with a number of expert evaluations. However, traditional FIDs can only process a single expert’s evaluation. The other is that they use incomprehensive evaluation criteria to score nodes in complex systems with many different relationships receiving the same score, which does not reflect their differences.Based on the fuzzy sets theory (FST) and Dempster–Shafer evidence theory (DST), this paper proposes for the fuzzy evidential influence diagram (FEID) to construct a new ID evaluation system and modify a corresponding algorithm. FEID allows multiple experts to evaluate nodes in IDs and can describe the differences between different nodes more exactly. Besides, two different fusion methods are used in the modified FEID evaluation algorithm. One approach uses the belief function and plausibility function to cover all possible outcomes while the other approach only provides the probability function in the convenience of human judgment. These two fusion methods can both be applied to the FEID evaluation algorithm in theory but they are suited for different application areas. Numerical examples expound the calculation process of the FEID evaluation algorithm and real applications in a supply chain financial (SCF) system and a tunnel construction (TC) system are used to compare the different fusion methods. The results given by the two fusion methods demonstrate which is better for analyzing this FEID. Anyway, compared to traditional FIDs, FEIDs can more accurately reflect the true situation and achieve more useful results.