Each fuzzy set can be represented by a nested system of ordinary sets—its a-cuts. There is an extensive literature on fuzzy sets devoted to problems of the following kind: is it possible to reduce operations with fuzzy sets to operations with their a-cuts? Is it possible to reduce properties of fuzzy relations to properties of their a-cuts? More generally, can a fuzzy concept be represented by ...

We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show th...

We study the Shannon information rate of accepting runs of various forms of automata. The rate is therefore a complexity indicator for executions of the automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, with computable execution rates. We also conduct ex...