Self-Learning Modeling in Possibilistic Model Checking

Generalized possibility Kripke structure (GPKS) plays a key role in modeling fuzzy systems for possibilistic model checking. However, it is unrealistic, in practice, to produce manually a large number of fuzzy states of GPKSs and transition relations over states space. In this article, we develop an online supervised learning algorithm for GPKS to learn its fuzzy states and possibilistic transition matrix. We assume that true fuzzy states of GPKSs are unknown, only available knowledge is the external (sensor's) variables that have ambiguous connections with the states. We connect the sensor's variables to the atomic propositions used to describe the fuzzy states through a family of (Gaussian) fuzzy functions. The first GPKS's learning model is called the GPKS with Fuzzifier Sets (GPKS-FS) that consists of a standard GPKS and a group of fuzzy functions that connect model's states to different sensor variables. The learning algorithm based on stochastic gradient descent is derived to learn all parameters of the (Gaussian) fuzzy functions and all elements of atomic propositions evolution matrix used to explain mechanism of transition between system's states. Based on the evolution matrix, we propose a method of constructing the similarity-based possibilistic transition matrix. This produces the possibilistic transition matrix which is critical for model checking over GPKSs. The learning algorithm do not rely on any subjective information from humans and remove a significant bottleneck for modeling of possibilistic model checking. Computer simulation results showing learning performance.