New directions in LB-valued general fuzzy automata: A topological view

Abstract

In the current study, we define the different L-valued operators on LB-valued general fuzzy automata or simply LB-valued GFA, where B is considered as a complete infinitely distributive lattice of propositions about the GFA. In particular, this study demonstrates that the L-valued successor and predecessor operators induce L-valued co-topologies while the L-valued residuated and approximation operators induce L-valued topologies on the state set of given LB-valued GFA. Further, we show that the continuity and separation properties of such LB-valued general fuzzy automaton can be examined in terms of these topologies. Moreover, we study and explicate the LB-valued GFA structure space and LB-valued GFA homotopy in more details.