Bi-Fuzzy Discrete Event Systems and Their Supervisory Control Theory

TL;DR

This paper introduces bi-fuzzy discrete event systems (BFDESs), a new model combining classical DESs and type-2 fuzzy sets to better handle high-uncertainty systems, along with supervisory control theory and algorithms.

Contribution

It proposes the BFDES model integrating T2 fuzzy sets with classical DESs and develops supervisory control theorems and algorithms for this new framework.

Findings

Bi-fuzzy controllability theorem established

An algorithm for checking bi-fuzzy controllability provided

Illustrative example demonstrates BFDES advantages

Abstract

It is well known that type-1 fuzzy sets (T1 FSs) have limited capabilities to handle some data uncertainties directly, and type-2 fuzzy sets (T2 FSs) can cover the shortcoming of T1 FSs to a certain extent. Fuzzy discrete event systems (FDESs) were proposed based on T1 FSs theory. Hence, FDES may not be a satisfactory model to characterize some high-uncertainty systems. In this paper, we propose a new model, called as bi-fuzzy discrete event systems (BFDESs), by combining classical DESs theory and T2 FSs theory. Then, we consider the supervisory control problem of BFDESs. The bi-fuzzy controllability theorem and nonblocking bi-fuzzy controllability theorem are demonstrated. Also, an algorithm for checking the bi-fuzzy controllability condition is presented. In addition, two controllable approximations to an uncontrollable language are investigated in detail. An illustrative example is provided to show the applicability and the advantages of BFDESs model.