Finite determinization of fuzzy automata using a parametric product-based t-norm
This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm diff...
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| Veröffentlicht in: | Fuzzy sets and systems Jg. 488; S. 108990 |
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15.07.2024
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| Abstract | This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm differs from the behavior of the fuzzy automaton over the product t-norm only in words with a degree of acceptance below the given parameter. However, using the parametric t-norm, we obtain an algorithm that outputs a finite minimal deterministic fuzzy automaton whose behavior differs from the starting fuzzy automaton described above. By setting the parameter to a sufficiently small value, the proposed algorithm provides a deterministic fuzzy automaton with behavior that differs insignificantly from the starting fuzzy automaton, as the difference is achieved only for words accepted by the starting fuzzy automaton with an insignificant value. As a tradeoff, the proposed approach provides finite determinization, even when all other determinization methods would result in an infinite deterministic automaton. We support this fact with an illustrative example. |
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| AbstractList | This paper presents a novel approach for the approximate determinization of fuzzy automata over the product structure. We introduce the parametric modification of the product t-norm in the pre-determinization setting. On the one hand, the behavior of a fuzzy automaton over the parametric t-norm differs from the behavior of the fuzzy automaton over the product t-norm only in words with a degree of acceptance below the given parameter. However, using the parametric t-norm, we obtain an algorithm that outputs a finite minimal deterministic fuzzy automaton whose behavior differs from the starting fuzzy automaton described above. By setting the parameter to a sufficiently small value, the proposed algorithm provides a deterministic fuzzy automaton with behavior that differs insignificantly from the starting fuzzy automaton, as the difference is achieved only for words accepted by the starting fuzzy automaton with an insignificant value. As a tradeoff, the proposed approach provides finite determinization, even when all other determinization methods would result in an infinite deterministic automaton. We support this fact with an illustrative example. |
| ArticleNumber | 108990 |
| Author | Ćirić, Miroslav González de Mendívil, José Ramón Jančić, Zorana Micić, Ivana Stanimirović, Stefan |
| Author_xml | – sequence: 1 givenname: Ivana surname: Micić fullname: Micić, Ivana email: ivana.micic@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia – sequence: 2 givenname: Stefan orcidid: 0000-0003-3126-1265 surname: Stanimirović fullname: Stanimirović, Stefan email: stefan.stanimirovic@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia – sequence: 3 givenname: José Ramón orcidid: 0000-0003-3150-6437 surname: González de Mendívil fullname: González de Mendívil, José Ramón email: mendivil@unavarra.es organization: Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, Campus de Arrosadia, Pamplona, 31006, Spain – sequence: 4 givenname: Miroslav orcidid: 0000-0001-8625-4682 surname: Ćirić fullname: Ćirić, Miroslav email: miroslav.ciric@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia – sequence: 5 givenname: Zorana orcidid: 0000-0002-7495-5534 surname: Jančić fullname: Jančić, Zorana email: zorana.jancic@pmf.edu.rs organization: University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, Niš, 18000, Serbia |
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| Keywords | Finite determinization Fuzzy automata Brzozowski's procedure Product t-norm Parametric t-norm Minimal deterministic fuzzy automaton |
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| References | Gonzalez de Mendívil (br0090) 2018; 26 Gerdjikov, Gonzalez de Mendívil (br0070) 2020; 397 Kirsten, Mäurer (br0200) 2005; 10 Li, Pedrycz (br0250) 2005; 156 Ignjatović, Ćirić, Bogdanović, Petković (br0140) 2010; 161 Jančić, Ćirić (br0160) 2014; 249 Jančić, Micić, Ignjatović, Ćirić (br0180) 2015; 301 Ignjatović, Ćirić (br0150) 2010; 180 de Mendívil Grau, Stanimirović, Fariña (br0040) 2023; 31 Lahaye, Lai, Komenda, Boimond (br0230) 2020; 30 Micić, Jančić, Ignjatović, Ćirić (br0260) 2015; 23 Bělohlávek (br0020) 2002; 143 de Mendívil Grau, Stanimirović, Fariña (br0050) 2023 Ignjatović, Ćirić, Bogdanović (br0130) 2008; 178 Rahonis (br0280) 2009 Gonzalez de Mendívil, Garitagoitia (br0110) 2014; 283 Jančić, Micić, Stanimirović, Gonzalez de Mendívil, Ćirić (br0190) 2023 Klement, Mesiar, Pap (br0210) 2013 Li (br0240) 2008; 47 Mohri (br0270) 1997; 23 Jančić, Ignjatović, Ćirić (br0170) 2011; 181 Gonzalez de Mendívil (br0080) 2016; 301 Stanimirović, Ćirić, Ignjatović (br0290) 2018; 469 Gonzalez de Mendívil, Garitagoitia (br0120) 2014; 249 Yang, Li (br0300) 2021; 420 (br0060) 2009 Alsina, Schweizer, Frank (br0010) 2006 Klir, Yuan (br0220) 1995 Ćirić, Droste, Ignjatović, Vogler (br0030) 2010; 180 Gonzalez de Mendívil, Fariña Figueredo (br0100) 2019; 376 Gonzalez de Mendívil (10.1016/j.fss.2024.108990_br0120) 2014; 249 Jančić (10.1016/j.fss.2024.108990_br0180) 2015; 301 Gonzalez de Mendívil (10.1016/j.fss.2024.108990_br0080) 2016; 301 Klir (10.1016/j.fss.2024.108990_br0220) 1995 Alsina (10.1016/j.fss.2024.108990_br0010) 2006 Lahaye (10.1016/j.fss.2024.108990_br0230) 2020; 30 Rahonis (10.1016/j.fss.2024.108990_br0280) 2009 Ignjatović (10.1016/j.fss.2024.108990_br0140) 2010; 161 Ignjatović (10.1016/j.fss.2024.108990_br0150) 2010; 180 de Mendívil Grau (10.1016/j.fss.2024.108990_br0050) 2023 Jančić (10.1016/j.fss.2024.108990_br0190) 2023 Gerdjikov (10.1016/j.fss.2024.108990_br0070) 2020; 397 Gonzalez de Mendívil (10.1016/j.fss.2024.108990_br0110) 2014; 283 Gonzalez de Mendívil (10.1016/j.fss.2024.108990_br0100) 2019; 376 Klement (10.1016/j.fss.2024.108990_br0210) 2013 Jančić (10.1016/j.fss.2024.108990_br0160) 2014; 249 Mohri (10.1016/j.fss.2024.108990_br0270) 1997; 23 de Mendívil Grau (10.1016/j.fss.2024.108990_br0040) 2023; 31 Kirsten (10.1016/j.fss.2024.108990_br0200) 2005; 10 Bělohlávek (10.1016/j.fss.2024.108990_br0020) 2002; 143 Li (10.1016/j.fss.2024.108990_br0250) 2005; 156 Ignjatović (10.1016/j.fss.2024.108990_br0130) 2008; 178 Gonzalez de Mendívil (10.1016/j.fss.2024.108990_br0090) 2018; 26 Ćirić (10.1016/j.fss.2024.108990_br0030) 2010; 180 (10.1016/j.fss.2024.108990_br0060) 2009 Micić (10.1016/j.fss.2024.108990_br0260) 2015; 23 Li (10.1016/j.fss.2024.108990_br0240) 2008; 47 Yang (10.1016/j.fss.2024.108990_br0300) 2021; 420 Jančić (10.1016/j.fss.2024.108990_br0170) 2011; 181 Stanimirović (10.1016/j.fss.2024.108990_br0290) 2018; 469 |
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