Fuzzy partitioned discrete-event system and its supervisory control

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, ${\mathcal{L}}_m^{{\mathsf{P}}_{\mathsf{A}}}$-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.

Keywords:

• Fuzzy partition
• fuzzy partitioned automata
• fuzzy partitioned discrete-event system
• supervisory control

Acknowledgements

The authors are greatly indebted to the Editor and the Referee(s) for their valuable observations and suggestions for improving the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author acknowledges the support of Science and Engineering Research Board (SERB), Ministry of Science & Technology, DST, Govt. of India, under grant No. EMR/2017/001108.

Notes on contributors

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.