Abstract
The aim of this article is to explain why we study fuzzy automata and how we do it, i.e., to highlight the most efficient tools of the theory of fuzzy sets that we use in our research. In addition, we want to show how research in the theory of fuzzy automata affected our research in other areas of the theory of fuzzy sets.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bělohlávek, R.: Determinism and Fuzzy Automata. Information Sciences 143, 205–209 (2002)
Ćirić, M., Droste, M., Ignjatović, J., Vogler, H.: Determinization of Weighted Finite Automata Over Strong Bimonoids. Information Sciences 180, 3497–3520 (2010)
Ćirić, M., Ignjatović, J., Bogdanović, S.: Fuzzy Equivalence Relations and Their Equivalence Classes. Fuzzy Sets and Systems 158, 1295–1313 (2007)
Ćirić, M., Ignjatović, J., Bogdanović, S.: Uniform fuzzy relations and fuzzy functions. Fuzzy Sets and Systems 160, 1054–1081 (2009)
Ćirić, M., Ignjatović, J., Damljanović, N., Bašić, M.: Bisimulations for Fuzzy Automata. Fuzzy Sets and Systems 186, 100–139 (2012)
Ćirić, M., Ignjatović, J., Jančić, I., Damljanović, N.: Computation of the Greatest Simulations and Bisimulations Between Fuzzy Automata. Fuzzy Sets and Systems 208, 22–42
Ćirić, M., Stamenković, A., Ignjatović, J., Petković, T.: Fuzzy Relation Equations and Reduction of Fuzzy Automata. Journal of Computer and Systems Sciences 76, 609–633 (2010)
Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata, Monographs in Theoretical Computer Science. EATCS Series. Springer (2009)
Ignjatović, J., Ćirić, M.: Weakly Linear Systems of Fuzzy Relation Inequalities and Their Applications: A Brief Survey. Filomat 26(2), 1–35 (2012)
Ignjatović, J., Ćirić, M., Bogdanović, S.: Determinization of Fuzzy Automata With Membership Values in Complete Residuated Lattices. Information Sciences 178, 164–180 (2008)
Ignjatović, J., Ćirić, M., Bogdanović, S.: Fuzzy Homomorphisms of Algebras. Fuzzy Sets and Systems 160, 2345–2365 (2009)
Ignjatović, J., Ćirić, M., Bogdanović, S.: On the Greatest Solutions to Weakly Linear Systems of Fuzzy Relation Inequalities and Equations. Fuzzy Sets and Systems 161, 3081–3113 (2010)
Ignjatović, J., Ćirić, M., Bogdanović, S., Petković, T.: Myhill-Nerode Type Theory for Fuzzy Languages and Automata. Fuzzy Sets and Systems 161, 1288–1324 (2010)
Ignjatović, J., Ćirić, M., Damljanović, N., Jančić, I.: Weakly Linear Systems of Fuzzy Relation Inequalities: The Heterogeneous Case. Fuzzy Sets and Systems (2011), doi:10.1016/j.fss.2011.11.011
Ignjatović, J., Ćirić, M., De Baets, B.: General Method for Solving Equations and Inequalities Defined by Residuated Functions (to appear)
Ignjatović, J., Ćirić, M., Simović, V.: Fuzzy Relation Equations and Subsystems of Fuzzy Transition Systems. Knowledge-based Systems (2012), doi:10.1016/j.knosys.2012.02.008
Jančić, Z., Ignjatović, J., Ćirić, M.: An Improved Algorithm for Determinization of Weighted and Fuzzy Automata. Information Sciences 181, 1358–1368 (2011)
Lee, E.T.-Z., Zadeh, L.A.: Note on Fuzzy Languages. Information Sciences 1, 421–434 (1969)
Li, Y., Pedrycz, W.: Fuzzy Finite Automata and Fuzzy Regular Expressions With Membership Values in Lattice Ordered Monoids. Fuzzy Sets and Systems 156, 68–92 (2005)
Peeva, K.: Behaviour, Reduction and Minimization of Finite L-automata. Fuzzy Sets and Systems 28, 171–181 (1988)
Peeva, K.: Finite L-fuzzy Machines. Fuzzy Sets and Systems 141, 415–437 (2004)
Peeva, K., Kyosev, Y.: Fuzzy Relational Calculus: Theory, Applications, and Software. World Scientific (2004)
Stamenković, A., Ćirić, M., Ignjatović, J.: Reduction of Fuzzy Automata by Means of Fuzzy Quasi-orders. Submitted to Information Sciences
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ćirić, M., Ignjatović, J. (2013). Fuzziness in Automata Theory: Why? How?. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35641-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-35641-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35640-7
Online ISBN: 978-3-642-35641-4
eBook Packages: EngineeringEngineering (R0)