The fuzzy automata are a mathematically disciplined way of modelling sequential processes. These processes are not crisp, but rather graded through their transitions, recognitions, and terminal responses. Classical formulations make use of a fixed aggregation operation which is either max-min or max-product composition. Thus, uncertainties are propagated uniformly throughout the computation. A paper presents a theoretical framework in which fuzzy automata are endowed with context-dependent triangular norms and interpreted through fuzzy topological structures. Connecting transition aggregation, fuzzy continuity, and convergence of state evolution in a single formal framework compatible with computational intelligence is the central aim. The paper undertakes a review of the core components of fuzzy sets, fuzzy relations, fuzzy automata, triangular norms, and fuzzy topology, before studying a context-sensitive t-norm fuzzy automaton in which the aggregation law may depend on an observable or latent context. A fuzzy topology induced by the transition is then defined on the state set, which facilitates the study of transition maps and acceptance functionals as fuzzy-continuous multi-maps. A number of basic propositions and theorems establish conditions for monotonicity, continuity with finite words, and convergence under regularity conditions. An example calculation shows that acceptance grades are manipulated according to a contextual t-norm. It is shown that such a topological reading enhances the understandability of fuzzy automata in adaptive reasoning systems, pattern recognition, approximate control, and other computational-intelligence applications where uncertainty is sequentially and contextually sensitive.
Kumar et al. (Fri,) studied this question.