| Title of paper:
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Reduced generalized nets with characteristics of the arcs
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| Author(s):
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| Velin Andonov
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| Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
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| velin_andonov@math.bas.bg
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| Published in:
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"Issues in Intuitionistic Fuzzy Sets and Generalized Nets", Volume 14 (2018/19), pages 25-35
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| Download:
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 PDF (199 Kb, File info)
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| Abstract:
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In most publications on the applications of Generalized Nets (GNs) in the modelling of real-life processes reduced GNs are used rather than ordinary GNs. The use of reduced GNs allows for a more simple general description of the model as only the minimal number of transition components, i.e. set of input places, set of output places and the Index Matrix (IM) of the transition’s condition are described. The reduced GNs have also huge theoretical significance because many theorems can be proved easily with the use ofreduced GNs. In recent years, the existence of two classes of minimal reduced GNs has been proven – one in which only the tokens obtain characteristics and one in which only the places obtain characteristics during the functioning of the net. In the present paper, a third class of minimal reduced GNs is proposed in which only the arcs obtain characteristics. Theorems for representation of the GNs from this class with minimal reduced GNs in which only the tokens receive characteristics are proved.
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| Keywords:
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Generalized nets, Reduced generalized nets, Generalized nets extensions.
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| References:
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- Andonov, V., Reduced generalized nets with characteristics of the places. International Journal “Information Models and Analyses”, Vol. 3, 2014, No. 2, 113–125.
- Andonov, V., Generalized Nets with Characteristics of the Arcs. Compt. rend. Acad. bulg. Sci., Vol. 70, 2017, No 10, 1341–1347.
- Andonov, V., K. Atanassov, Generalized nets with characteristics of the places. Compt. rend. Acad. bulg. Sci., Vol. 66, 2013, No. 12, 1673–1680.
- Andonov, V., A. Shannon, Intuitionistic fuzzy evaluation of the behavior of tokens in generalized nets. Advances in Intelligent Systems and Computing, Springer, Vol. 322, 2015, 633–644.
- Andonov, V., N. Angelova, Modifications of the algorithms for transition functioning in GNs, GNCP, IFGNCP1 and IFGNCP3 when merging of tokens is permitted. Springer Series Studies in Fuzziness and Soft Computing, 2015, 275–288.
- Atanassov, K., Generalized Nets. World Scientific, Singapore, London, 1991.
- Atanassov, K., On Generalized Nets Theory. Prof. M. Drinov Academic Publ. House, Sofia, 2007.
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