Abstract
This paper is towards the study of a fuzzy partitioned discrete-event system and its supervisory control theory under partial/full observations. Specifically, we study the concept of a fuzzy partitioned automaton corresponding to a given fuzzy automaton and use it to model the fuzzy partitioned discrete-event system. The behavior of such fuzzy partitioned discrete-event system is modeled by fuzzy language, which is generated by a fuzzy partitioned automaton. Further, we introduce the model of controlled systems of a fuzzy partitioned discrete-event system under (partially/fully observable) fuzzy supervisors. Furthermore, we establish the relationships between the fuzzy languages generated/marked by controlled systems and controllable, observable, -closed fuzzy languages. Moreover, we discuss the supremal/infimal controllable fuzzy languages and an infimal controllable, observable fuzzy language. Besides, we provide an application of the fuzzy partitioned discrete-event system in a real-life problem.
Acknowledgements
The authors are greatly indebted to the Editor and the Referee(s) for their valuable observations and suggestions for improving the paper.
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Shailendra Singh
Shailendra Singh obtained his Master's degree in Mathematics from the University of Lucknow, Lucknow, India in 2015. He is currently a PhD student in the Department of Mathematics & Computing, IIT(ISM), Dhanbad, India. His research interests include topology, category theory, and fuzzy automata with its languages.
S. P. Tiwari
S. P. Tiwari is an Associate Professor in Department of Mathematics & Computing, IIT(ISM) Dhanbad, Dhanbad, India. He received his Master degree from Dr. R.M.L. Avadh University, Faizabad, India, and the Ph.D. degree from Banaras Hindu University, Varanasi, India. He is a member of American Mathematical Society, life member of Indian Mathematical Society and Board Member of European Society for Fuzzy Logic and Technology for 2017-2021. His area of research includes automata theory, rough set theory, category theory and topology.