Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bou...

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

This paper presents a contribution to minimization of intuitionistic fuzzy automata. In this paper the concept of substitution property (SP) partition for a finite intuitionistic fuzzy automaton is formulated, and the quotient automaton with respect to an SP partition is defined.

In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

In this note first by considering the notion of general fuzzy automata (for simplicity GFA), we define the notions of direct product, restricted direct product and join of two GFA. Also, we introduce some operations on (Fuzzy) sets and then prove some related theorems. Finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given GFA....

After the research on naBL-algebras gained by non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of generalization BL-algebras, which can be obtained general functions. In this paper, we show that not every function induce an BL-algebra counterexample thus propose new concept weak BL-algebras. We prove each corresponds to BL-algebra; there...

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is ...

In this paper, at first, we define the notion of general fuzzy automaton over a field; call vector (VGFA). Moreover, present concept max-min automaton. We show that if two VGFA are similar, they constitute an isomorphism. After that, prove isomorphism with threshold α, equivalent where $\alpha \in [0,1]$. Also, some examples given to clarify these new notions.

General automata are considered with respect to normal-ization over semirings. Possibilistic automata are deened as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochas-tic automata where stochastic (+=) semirings are replaced by possi-bilistic (_=^) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata)...