Hierarchical weighted fuzzy Petri nets and their application for transport logistics problem

Modeling of Passenger Transport Logistics Based on Intelligent Computational Techniques

“…If w ij is equal to "1" then there is the strongest possible connection. If w ij is "0" then there is no connection between the given object and the corresponding property [12][13][14][15].…”

“…Papers [13][14][15] challenged the authors with the problem of the change of decisions with the change of triples. For this reason, the authors applied two strategies: (1) to apply all other combinations of triples which are in between previously chosen couple of triples for the analysis of truth probability of their resulting outputs (i.e., the preferred triple of function from the couple is the one that has the same decision as the decision achieved by the majority of triple of functions in between); (2) to find the average mathematical meaning of every resulting output place which is associated with the corresponding object after applying all the chosen triples of functions [15].…”

“…The application of weights in FPN (wFPN) which aims to achieve the most concretized numerical result at every output place for the net was presented in the following papers [12][13][14][15]. Additionally, an optimized triple of functions (ZtN, ZtN, LsN) for the research with its implementation and a proof of its mathematical effectiveness over a classic one (ZtN, GtN, ZsN) were presented [12,14,15]. Since papers [11,12] gave consistent decisions of the part of PTL scheme, they raised a need to present a hierarchical FPN conception for covering the whole PTL scheme in the future [16].…”

“…Additionally, an optimized triple of functions (ZtN, ZtN, LsN) for the research with its implementation and a proof of its mathematical effectiveness over a classic one (ZtN, GtN, ZsN) were presented [12,14,15]. Since papers [11,12] gave consistent decisions of the part of PTL scheme, they raised a need to present a hierarchical FPN conception for covering the whole PTL scheme in the future [16]. Along with the development of this theory and the possibility of practical implementation in wFPN, the scheme of PTL levels was presented [11].…”

“…Three-level hierarchical structure of wFPN with additional separate model for PTL was proposed with the application of the three classic triangular norms mentioned above [13].…”