J. Math. Computer Sci., 30 (2023), 89–100 Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Regular string token fuzzy Petri nets A. John Kaspar, D. K. Sheena Christy ∗ Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, 6032 203, India. Abstract Fuzzy Petri nets are a type of classical Petri nets designed to deal with imprecise and ambiguous data, that have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, we introduce a new model called string token fuzzy Petri nets to generate fuzzy regular languages. Also, we study the equivalences of fuzzy regular grammar and regular string token fuzzy Petri net and establish some closure properties such as union, catenation, kleene closure, reversal, homomorphism and inverse homomorphism of the languages generated by the regular string token fuzzy Petri nets. Keywords: Fuzzy Petri net, Petri net languages, string token Petri net, fuzzy languages. 2020 MSC: 68Q45. ©2023 All rights reserved. 1. Introduction The concept of formal language was first introduced and discussed by linguist, Noam Chomsky in [6]. A formal language is a set of sequence of symbols over some finite alphabet and the formal languages are generated or recognized by abstract devices. Some of the major and useful devices to generate formal languages are formal grammars (regular, context-free and context-sensitive), Petri nets, L-systems and automata [14, 17, 29]. Later various classes of formal languages were introduced, also their relation with its generating devices are initiated and examined. Formal grammars generally called as grammars are precise description of formal languages, that is a grammar is a set of rules for rewriting strings to produce a language and the rewriting begins from a start symbol. The in-depth knowledge of formal languages along with its application in several fields such as pattern matching, syntax, lexical analyzer, picture recognition etc, and its relation with grammars can be found in [14, 28]. Recently, there is an increasing interest in studying and analyzing grammars and Petri nets, which are more applicable and effective devices to generate the formal languages. Petri nets are dynamic graph with two disjoint sets of nodes of which first includes the places represented by circles and the second are transitions represented by rectangles [27]. A Petri net is used to create a simple mathematical framework for modelling concurrent systems and their behaviour. The collection of firing sequences of transitions produced by the Petri net is the primary importance in many applications of Petri nets. In addition to that, they have been used for the description and analysis of system of parallel process [25, 30, 31]. Among the distinct varieties of Petri nets ∗ Corresponding author Email addresses: ja8952@srmist.edu.in (A. John Kaspar), sheena.lesley@gmail.com (D. K. Sheena Christy) doi: 10.22436/jmcs.030.02.01 Received: 2022-04-25 Revised: 2022-10-23 Accepted: 2022-11-10