A Linguistic Extension of Petri Nets for the Description of Systems: An Application to Time Series

Time series (TSs) are usually represented numerically; however, there are many situations where a linguistic description is preferable. Granular linguistic model of phenomena (GLMP) is a paradigm used in the generation of linguistic descriptions of static situations without considering the temporal relationship of data present, for example, in TSs. This paper presents a new method to generate linguistic descriptions of TSs with an operation similar to petri nets (PNs) and inspired by GLMP. The presented approach maintains the operation of PNs, adding a mechanism to generate linguistic descriptions based on GLMP. The main components of GLMP are added to places and transitions of PNs. This extension is called linguistic PNs (LPNs) and is a language that can be used to generate linguistic descriptions of systems. GLMP is a method that can be used by experts to design how the linguistic descriptions are synthesized and generated. So, LPNs also allow incorporating expert knowledge and combining descriptions in an appropriate way. The experimental part is focused on showing how LPNs can be used to linguistically describe TSs, including the occurrence of maxima or minima, and trends.