Bayesian Linguistic Conditional System as an Attention Mechanism in a Failure Mode and Effect Analysis

Abstract

Fuzzy Inference System behavior can be described qualitatively using a natural language, which is known as the expert-driven approach to handling non-statistical uncertainty. Generally, practical applications involve conceptualizing the problem by integrating linguistic uncertainty and using data by integrating stochastic uncertainty. The proposed probabilistic fuzzy system uses the Gaussian Density Function (GDF) to assign a probability to input variables integrating stochastic uncertainty. In addition, a linguistic interpretation is used to project various categories of the GDF integrating linguistic uncertainty. Likewise, one of the relevant aspects of the proposal is to weigh each input variable according to the heuristic interpretation that determines the probability assigned to each of them a priori. Therefore, the main contribution of the research focuses on using the Bayesian Linguistic Conditional System (BLCS) as a mechanism of attention to relate the categories of the different input variables and find their posterior-weighted probability at a normalization stage. Finally, the knowledge base is established through linguistic rules, and the system’s output is a Bayesian classifier multiplying its normalized posterior conditional probabilities. The highest probability value of the knowledge base is identified, and the Risk Priority Number Weighted (RPNW) is determined using their respective posterior-normalized probabilities for each input variable. The results are expressed on a simple and precise scale from 1 to 10. They are compared with the Risk Priority Number (RPN), which results in a Failure Mode and Effect Analysis (FMEA). They show similar behaviors for multiple combinations in the evaluations while highlighting different scales.