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Isomorphism Between Two Vector General Fuzzy Automata
Volume 34, Issue 3 (2023), pp. 617–633
Marzieh Shamsizadeh ORCID icon link to view author Marzieh Shamsizadeh details   Ehsan Movahednia   Manuel De la Sen  

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https://doi.org/10.15388/23-INFOR514
Pub. online: 23 March 2023      Type: Research Article      Open accessOpen Access

Received
1 July 2022
Accepted
1 March 2023
Published
23 March 2023

Abstract

In this paper, at first, we define the notion of general fuzzy automaton over a field; we call this automaton vector general fuzzy automaton (VGFA). Moreover, we present the concept of max-min vector general fuzzy automaton. We show that if two max-min VGFA are similar, they constitute an isomorphism. After that, we prove that if two VGFA constitute an isomorphism with threshold α, they are equivalent with threshold α, where $\alpha \in [0,1]$. Also, some examples are given to clarify these new notions.

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Biographies

Shamsizadeh Marzieh
https://orcid.org/0000-0001-9320-9433
shamsizadeh.m@gmail.com

M. Shamsizadeh is an assistant professor in the Mathematics Department at Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran. She is a mathematician and her main goal is to bring novel perspectives to complex problems at the intersection of different branches of mathematics. Her main interests in mathematics are graph theory, automata theory, and fuzzy logic.

Movahednia Ehsan
movahednia@bkatu.ac.ir

E. Movahednia is an assistant professor of mathematics at Khatam Alnbia University of Technology in Behbahan, Iran. He has over 10 years of experience in academia and specializes in the stability of functional equations, fuzzy mathematics, fixed point theory, and Banach algebra. His research focuses on developing innovative mathematical models and methods to solve real-world problems in engineering, biology, and computer science. He has published his work in top international journals and presented his findings at multiple conferences globally.

De la Sen Manuel
manuel.delasen@ehu.es

M. De la Sen was born in Arrigorriaga, Bizkaia, in the Spanish Basque Country. He obtained the MSc degree with honours from the University of the Basque Country in 1979, the PhD degree in applied physics with high honours from the same University in 1979 and the degree of Docteur-d’ Etat-ès-Sciences Physiques (specialité Automatique et Traitement du Signal) from the Université de Grenoble, France, with “mention très honorable” in 1987. He is currently a professor of systems engineering and automatic control in the Department of Electricity and Electronics of the University of the Basque Country and head of the Institute of Research and Development of Processes (IIDP). He also had positions of visiting professor in the University of Grenoble (France), the University of Newcastle (New South Wales, Australia) and the Australian National University ANU (Canberra, Australia). He is currently a member of several editorial boards of scientific journals. He has been an author or co-author of more than one thousand of papers in the fields of adaptive systems, mathematical systems theory, mathematical models in biology and epidemic mathematical models, fixed point theory, and ordinary differential equations and discrete equations, which are his main research interests.


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Keywords
fuzzy automata linear automata vector automata general fuzzy automata Similar

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