In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length h. Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. \blue{The proposed approach consists in exploiting} a subset of h observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a "forgetfulness" of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As \blue{the} analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these \blue{irrelevant} basis markings based on linear programming is proposed.
This article introduces a floppy logic – a new method of work with fuzzy sets. This theory is a nice connection between the logic, the probability theory and the fuzzy sets. The floppy logic has several advantages compared to the fuzzy logic: All propositions, which are equivalent in the bivalent logic, are equivalent in the floppy logic too. Logical operations are modeled unambiguously, not by using many alternative t-norms and t-conorms. In floppy logic, we can use the whole apparatus of Kolmogorov’s probability theory. This theory allows to work consistently with systems that are described by fuzzy sets, probability distributions and accurate values simultaneously.