On \(R\)-fuzzy Petri nets. (Spanish. English summary) Zbl 0951.68097

Summary: In a recent electronic preprint J. S. Golan [A framework for consideration of fuzzy Petri nets, Proceedings of FUZZY’97 International Conference on Fuzzy Logic and Applications, Zikhon Yaakov (1997) (http://mathcs3.haifa.ac.il/math/golan-preprints.html)] asks about the structure of the left \(R\)-semimodule formed by all the \(R\)-fuzzy Petri nets over an ordered pair of nonempty disjoint sets, being \(R\) a semiring with identity element and free of zero sums. The fundamental purpose of this paper is to present an answer to this problem in terms of category theory. Two contravariant functors, both defined over the category of ordered pairs of nonempty disjoint sets and with values in the category of left \(R\)-semimodules, are also studied and the existence of a natural isomorphism between them is proved.


68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
94C99 Circuits, networks
Full Text: EuDML EMIS