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Computation of Solutions to Certain Nonlinear Systems of Fuzzy Relation Inequations

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Algebraic Informatics (CAI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13706))

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Abstract

Although fuzzy relation equations and inequations have a broad field of application, it is common that they have no solutions or have only the trivial solution. Therefore, it is desirable to study new types of fuzzy relation inequations similar to the well-studied ones and with nontrivial solutions. This paper studies fuzzy relation inequations that include the degree of subsethood and the degree of equality of fuzzy sets. We provide formulae for determining the greatest solutions to systems of such fuzzy relation inequations. We provide alternative ways to compute these solutions when we cannot run the methods based on these formulae.

This research was supported by the Science Fund of the Republic of Serbia, GRANT No 7750185, Quantitative Automata Models: Fundamental Problems and Applications - QUAM, and by Ministry of Education, Science and Technological Development, Republic of Serbia, Contract No. 451-03-68/2022-14/200124.

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References

  1. Bartl, E.: Minimal solutions of generalized fuzzy relational equations: probabilistic algorithm based on greedy approach. Fuzzy Sets Syst. 260, 25–42 (2015)

    Article  MathSciNet  Google Scholar 

  2. Bartl, E., Belohlavek, R.: Sup-t-norm and inf-residuum are a single type of relational equations. Int. J. Gen Syst 40(6), 599–609 (2011)

    Article  MathSciNet  Google Scholar 

  3. Bartl, E., Klir, G.J.: Fuzzy relational equations in general framework. Int. J. Gen Syst 43(1), 1–18 (2014)

    Article  MathSciNet  Google Scholar 

  4. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, New York (2002)

    Book  Google Scholar 

  5. Bělohlávek, R., Vychodil, V.: Fuzzy Equational Logic. Studies in Fuzziness and Soft Computing. Springer, Berlin-Heidelberg (2005). https://doi.org/10.1007/b105121

    Book  MATH  Google Scholar 

  6. Damljanović, N., Ćirić, M., Ignjatović, J.: Bisimulations for weighted automata over an additively idempotent semiring. Theoret. Comput. Sci. 534, 86–100 (2014)

    Article  MathSciNet  Google Scholar 

  7. Díaz-Moreno, J.C., Medina, J., Turunen, E.: Minimal solutions of general fuzzy relation equations on linear carriers. An algebraic characterization. Fuzzy Sets Syst. 311(C), 112–123 (2017)

    Article  MathSciNet  Google Scholar 

  8. Ignjatović, J., Ćirić, M.: Weakly linear systems of fuzzy relation inequalities and their applications: a brief survey. Filomat 26(2), 207–241 (2012)

    Article  MathSciNet  Google Scholar 

  9. Ignjatović, J., Ćirić, M., Bogdanović, S.: On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations. Fuzzy Sets Syst. 161(24), 3081–3113 (2010)

    Article  MathSciNet  Google Scholar 

  10. Ignjatović, J., Ćirić, M., Damljanović, N., Jančić, I.: Weakly linear systems of fuzzy relation inequalities: the heterogeneous case. Fuzzy Sets Syst. 199, 64–91 (2012)

    Article  MathSciNet  Google Scholar 

  11. Micić, I., Nguyen, L.A., Stanimirović, S.: Characterization and computation of approximate bisimulations for fuzzy automata. Fuzzy Sets Syst. 442, 331–350 (2022)

    Article  MathSciNet  Google Scholar 

  12. Micić, I., Stanimirović, S., Jančić, Z.: Approximate positional analysis of fuzzy social networks. Fuzzy Sets Syst. (2022). https://doi.org/10.1016/j.fss.2022.05.008

    Article  Google Scholar 

  13. Sanchez, E.: Equations de relations floues. Ph.D. thesis, Faculté de Médecine de Marseille (1974)

    Google Scholar 

  14. Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30(1), 38–48 (1976)

    Article  MathSciNet  Google Scholar 

  15. Stanimirović, S., Micić, I., Ćirić, M.: Approximate bisimulations for fuzzy automata over complete heyting algebras. IEEE Trans. Fuzzy Syst. 30, 437–447 (2022)

    Article  Google Scholar 

  16. Stanimirović, S., Stamenković, A., Ćirić, M.: Improved algorithms for computing the greatest right and left invariant boolean matrices and their application. Filomat 33(9), 2809–2831 (2019)

    Article  MathSciNet  Google Scholar 

  17. Stanimirović, S., Micić, I.: On the solvability of weakly linear systems of fuzzy relation equations. Inf. Sci. 607, 670–687 (2022)

    Article  Google Scholar 

  18. Turunen, E.: Necessary and sufficient conditions for the existence of solution of generalized fuzzy relation equations \(A \Leftrightarrow X = B\). Inf. Sci. 536, 351–357 (2020)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science and Mathematics, University of Niš, Niš, Serbia

    Ivana Micić, Zorana Jančić & Stefan Stanimirović

Authors
  1. Ivana Micić
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  2. Zorana Jančić
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  3. Stefan Stanimirović
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Corresponding author

Correspondence to Stefan Stanimirović .

Editor information

Editors and Affiliations

  1. Aristotle University of Thessaloniki, Thessaloniki, Greece

    Dimitrios Poulakis

  2. Aristotle University of Thessaloniki, Thessaloniki, Greece

    George Rahonis

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Micić, I., Jančić, Z., Stanimirović, S. (2022). Computation of Solutions to Certain Nonlinear Systems of Fuzzy Relation Inequations. In: Poulakis, D., Rahonis, G. (eds) Algebraic Informatics. CAI 2022. Lecture Notes in Computer Science, vol 13706. Springer, Cham. https://doi.org/10.1007/978-3-031-19685-0_14

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  • DOI: https://doi.org/10.1007/978-3-031-19685-0_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19684-3

  • Online ISBN: 978-3-031-19685-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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