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Reduction Graph for Minimal Determinization of Fuzzy Automata

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Fuzzy Logic and Technology, and Aggregation Operators (EUSFLAT 2023, AGOP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14069))

Abstract

We introduce a minimal determinization procedure for fuzzy finite automata (FfAs) with membership values in a complete residuated lattice (CRL). The method is based on the well-known determinization method via factorization of fuzzy states. However, different to other determinization methods, we do not assume that the CRL is zero divisors free. This fact requires modifying the functions that define the factorization to avoid the zero divisor values when creating the fuzzy states in the determinization procedure. After generating a right-irreducible fuzzy deterministic finite automaton (FDfA) equivalent to the original FfA by determinization via factorization, we construct the so-called reduction graph of this fuzzy automaton, where each arc represents the notion that a fuzzy state is left-reducible by another fuzzy state. By making these left-reductions, we obtain the equivalent minimal FDfA. It is worth mentioning that an empty fuzzy state is always reducible by a nonempty fuzzy state. This behavior, specific for a CRL with zero divisors, has also to be taken into account when the state reduction is carried out.

S. Stanimirović acknowledges the support of the Science Fund of the Republic of Serbia, GRANT No. 7750185, Quantitative Automata Models: Fundamental Problems and Applications - QUAM, and the Ministry of Education, Science and Technological Development, Republic of Serbia, Contract No. 451-03-68/2022-14/200124.

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Authors and Affiliations

  1. Depto. Estadística, Informática y Matemáticas, Univeridad Pública de Navarra, Campus de Arrosadía, 31006, Pamplona, Spain

    Aitor G. de Mendívil Grau & Federico Fariña

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Stefan Stanimirović

Authors
  1. Aitor G. de Mendívil Grau
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  2. Stefan Stanimirović
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  3. Federico Fariña
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Corresponding author

Correspondence to Aitor G. de Mendívil Grau .

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Editors and Affiliations

  1. University of the Balearic Islands, Palma, Spain

    Sebastia Massanet

  2. University of Oviedo, Gijón, Spain

    Susana Montes

  3. University of the Balearic Islands, Palma, Spain

    Daniel Ruiz-Aguilera

  4. University of the Balearic Islands, Palma, Spain

    Manuel González-Hidalgo

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de Mendívil Grau, A.G., Stanimirović, S., Fariña, F. (2023). Reduction Graph for Minimal Determinization of Fuzzy Automata. In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_45

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  • DOI: https://doi.org/10.1007/978-3-031-39965-7_45

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