Abstract
The paper describes the analysis of the application of classic and optimized triangular norms in the hierarchical structure of weighted fuzzy Petri nets on the example of passenger transport logistics. The research is presented in a scheme with several levels of tasks. Each task includes some knowledge sets which were previously given by the experts and set into tables of “Object–property” type. It leads to the creation of a hierarchical structure of weighted fuzzy Petri net model which includes 125 possible combinations of triples of functions for calculation processing. A classic triple of functions (ZtN, GtN, ZsN) is tested and compared with an optimized triple (ZtN, ZtN, LsN). Additional verification methods are applied to confirm the practical usefulness of these triples. These techniques imply the use of additional triples which can be associated with each other along with practically efficient mathematical calculations.
Highlights
The decision-support systems are becoming increasingly applied in different areas of life with the development of intelligent computational techniques
The decisions are as follows: “Lufthansa” as the best transport company of the aviation branch and “Business” as the best class of comfort for the previously chosen airline company. Another approach that is supposed to be tested is the hierarchical structure of weights in FPN (wFPN) models with application of an optimized triple of functions (ZtN, ZtN, LsN)
This section analyzes the achieved decisions by the classic triple (ZtN, GtN, Zadeh s-norm (ZsN)) and optimized one (ZtN, ZtN, LsN) in the hierarchical structures presented in Figs. 15 and 16 with additional models depicted in Figs. 13 and 17, respectively
Summary
The decision-support systems are becoming increasingly applied in different areas of life with the development of intelligent computational techniques. The authors present the research on the application of different triangular norms in the hierarchical structure of fuzzy Petri nets (FPN) for the analysis of the passenger transport logistics (PTL). The main feature of these nets is that they effectively support the structural organization of information, provide knowledge-based visualization of inference, and facilitate the design of efficient fuzzy inference algorithms All this makes FPNs a useful methodology for knowledge modeling and inference in decision-support systems [9, 10]. 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] Another approach which needed to be tested applied an optimized triple of functions (ZtN, ZtN, LsN) on the same scheme for the whole hierarchy [14]. All models are simulated in a special PNeS® software [17]
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