1 research outputs found
Reduction of fuzzy automata by means of fuzzy quasi-orders
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.Comment: 42 pages, submitted to Information Science