**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33035

##### The Analysis of Different Classes of Weighted Fuzzy Petri Nets and Their Features

**Authors:**
Yurii Bloshko,
Oksana Olar

**Abstract:**

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

**Keywords:**
Fuzzy petri net,
intelligent computational techniques,
knowledge representation,
triangular norms.

**References:**

[1] Z. Suraj, O. Olar, and Y. Bloshko, “Conception of fuzzy Petri net to solve transport logistics problems”, in Current Research in Mathematical and Computer Sciences II, Publisher UWM, Olsztyn, 2018, pp. 303-313.

[2] Z. Suraj, O. Olar, and Y. Bloshko, “Optimized fuzzy Petri nets and their application for transport logistics problem”, in Proc. Int. Workshop on CS&P, 2019, Olsztyn, Poland.

[3] Z. Suraj, O. Olar, and Y. Bloshko, “Hierarchical weighted fuzzy Petri nets and their application for transport logistics problem”, in Proc. Int. Conference on Intell. Syst. and Knowl. Eng., Cologne, Germany.

[4] Z. Suraj, O. Olar, and Y. Bloshko, “The Analysis of Human Oriented System of Weighted Fuzzy Petri Nets for Passenger Transport Logistics Problem”, in Advances in Intelligent Systems and Computing 1197, pp. 1580-1588, Springer, 2021.

[5] Z. Suraj, O. Olar and Y. Bloshko, “The Analysis of Triples of Triangular Norms for the Subject Area of Passenger Transport Logistics in Trends and Applications in Information Systems and Technologies, Advances in Intelligent Systems and Computing 1365, Vol. 1, Springer, pp. 29-38, Springer, 2021.

[6] Y. Bloshko, Z. Suraj and O. Olar, “Towards Optimization of Weighted Fuzzy Petri Nets for Hierarchical Application in the Subject Area of Passenger Transport Logistics”, 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2021), Luxembourg, 11-14 July, 2021, pp. 107-112, IEEE, 2021.

[7] Z. Suraj, O. Olar and Y. Bloshko, “The Influence of Fuzzy Expectations on Triples of t-/s-norms in the Weighted Fuzzy Petri Net for the Subject Area of Passenger Transport Logistics”, in Lecture Notes in Artificial Intelligence 12872, pp. 134-148, Springer Nature, 2021.

[8] Z. Suraj, O. Olar and Y. Bloshko, “Modeling of Passenger Transport Logistics Based on Intelligent Computational Techniques” in International Journal of Computational Intelligence Systems 14, 173, 2021.

[9] Z. Suraj and P. Grochowalski, “Petri nets and PNeS in modeling and analysis of concurrent systems”, in Proc. Int. Workshop on CS&P, 2017, Warsaw, pp. 1-12.

[10] R. David and H. Alla, “Petri nets and Grafcet: Tools for modelling discrete event systems”. Prentice Hall, 1992

[11] Z. Suraj, “A new class of fuzzy Petri nets for knowledge representation and reasoning”, Fundam. Inform., 128(1-2):193-207, 2013.

[12] H.-C. Liu et al., “Fuzzy Petri nets for knowledge representation and reasoning: A literature review”, Eng. Appl. Artif. Intell., 60:45-56, 2017.

[13] Z. Suraj, A.E. Hassanien, „Fuzzy Petri Nets and Interval Analysis Working Together”. Studies in Fuzziness and Soft Computing 377, pp. 395-413, Springer, 2018.

[14] Z. Suraj, “Toward optimization of reasoning using generalized fuzzy Petri nets”, LNAI 11103, pp. 294-308, Springer, 2018.

[15] Looney, C.G.: Fuzzy Petri nets for rule-based decision making. IEEE Trans. Syst. Man Cybern. 18(1), 178–183 (1988)

[16] S.-M. Chen: “Weighted fuzzy reasoning using weighted fuzzy Petri nets”, IEEE Trans. Knowl. Data Eng. 14(2), pp. 386-397, 2002.

[17] Cheng Xuezhen, Lin Xiaoxiao, Zhu Chunhua, Chen Qiang, Cao Maoyong, “Power System Fault Analysis Based on Hierarchical Fuzzy Petri Net Considering Time Association Character”, Transactions of China Electrotechnical Society, Vol. 32(14), pp. 229-237, 2017.

[18] Z. Suraj, A.E. Hassanien, S. Bandyopadhyay, “Weighted generalized fuzzy petri nets and rough sets for knowledge representation and reasoning, in Lecture Notes in Computer Science, vol. 12179, pp. 61–77. Springer, 2020

[19] V. Lyashkevych, O. Olar, and M. Lyashkevych, “Software ontology subject domain intelligence diagnostics of computer means”, in Proc. IEEE Int. Conference on Intelligent Data Acquisition and Advanced Computing Systems, 2013, Berlin, pp. 12-14

[20] V. Lokazyuk, O. Olar, and M. Lyashkevych. “Software for creating knowledge base of intelligent systems of diagnosing process”, in Advanced Computer System and Networks: Design and Application, 2009, Lviv, pp. 140-145.

[21] E. P. Klement, R. Mesiar, and E. Pap, “Triangular Norms”, Kluwer, 2000.

[22] O. Yaqub, L. Li, “Modeling and Analysis of Connected Traffic Intersections Based on Modified Binary Petri Nets. International Journal of Vehicular Technology”, Vol. 2013, Article ID 192516, 10 pages, 2013

[23] Z. Suraj, “Parameterised Fuzzy Petri Nets for Approximate Reasoning in Decision Support Systems”, Communications in Computer and Information Science 322, pp. 33-42, Springer, 2012.

[24] Z. Suraj: “Parameterised Fuzzy Petri Nets for Knowledge Representation and Reasoning”, in Joaquim Filipe, et al. (Eds.), Proceedings of the 2nd International Conference on Data Management Technologies and Applications (DATA 2013), Reykjavik, Iceland, 29-31 July, 2013, SCITEPRESS, Portugal, pp. 5-13, 2013.

[25] Suraj Z., Grochowalski, P., “Fuzzy Petri Nets with Linear Orders for Intervals”, in Lecture Notes in Computer Science 10687, Springer, 2017.

[26] Z. Xu, R. Yager, “Some geometric aggregation operators based on intuitionistic fuzzy sets”. Int. J. Gen. Syst. (35), pp. 413-417, 2006.

[27] Z. Suraj, P. Grochowalski, S. Bandyopadhyay, “Flexible Generalized Fuzzy Petri Nets for Rule-based Systems”. Lecture Notes in Comput. Sci. 10071, Springer, 2016.

[28] A. Skowron, “Boolean reasoning for decision rules generation”. LNAI 689, pp. 295-305, Springer, 1993.