Fuzzy Petri Nets with Linear Orders for Intervals

Recently, an extended class of generalized fuzzy Petri nets (GFP-nets) called type-2 generalized fuzzy Petri nets (T2GFP-nets) were proposed. This class extends the existing GFP-nets by introducing a triple of operators (In, Out(1), Out(2)) in a T2GFP-net in the form of interval triangular norms, which are supposed to function as substitute for the triangular norms in GFP-nets. In this paper we enrich the T2GFP-net model by adding to it instead of the usual partial order relation between interval numbers some of the most used examples of total orders that appear in the literature. This addition has significant influence on extending the use of T2GFP-nets in many different fields. In particular, the proposed approach can be used in intelligent control design, approximate reasoning, decision making or classification.