Reduction of fuzzy automata by means of fuzzy quasi-orders

TL;DR

This paper explores how fuzzy quasi-orders can improve state reduction in fuzzy automata, outperforming fuzzy equivalences, and relates these reductions to determinization and conflict analysis in fuzzy systems.

Contribution

It demonstrates that fuzzy quasi-orders, especially invariant ones, can lead to better reductions than fuzzy equivalences and connects these methods to determinization and conflict analysis.

Findings

Fuzzy quasi-orders can outperform fuzzy equivalences in state reduction.

Invariant fuzzy quasi-orders provide better reductions than equivalences.

Weakly invariant fuzzy quasi-orders relate to determinization and conflict analysis.

Abstract

In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi-orders. Generally, fuzzy quasi-orders and fuzzy equivalences are equally good in the state reduction, but we show that right and left invariant fuzzy quasi-orders give better reductions than right and left invariant fuzzy equivalences. We also show that alternate reductions by means of fuzzy quasi-orders give better results than alternate reductions by means of fuzzy equivalences. Furthermore we study a more general type of fuzzy quasi-orders, weakly right and left invariant ones, and we show that they are closely related to determinization of fuzzy recognizers. We also demonstrate some applications of weakly left invariant fuzzy quasi-orders in conflict analysis of fuzzy discrete event systems.