Categories of Automata and Languages Based on a Complete Residuated Lattice

Vinay Gautam (), S. P. Tiwari, Priyanka Pal () and Jayanti Tripathi ()
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Vinay Gautam: Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
S. P. Tiwari: Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
Priyanka Pal: Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
Jayanti Tripathi: Amity Institute of Applied Science (AIAS), Amity University, Noida 201313, Uttar Pradesh, India

New Mathematics and Natural Computation (NMNC), 2018, vol. 14, issue 03, 423-444

Abstract: The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category. Finally, we establish a construction of a minimal fuzzy automaton for a given fuzzy language in a categorical framework. The construction of such fuzzy automaton is based on derivative of a given fuzzy language.

Keywords: Fuzzy automaton; fuzzy language; derivative; minimal fuzzy realization (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S1793005718500254

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