State reduction of fuzzy automata has been studied by many authors. All of them have dealt with classical fuzzy automata over the Gödel structure and reduction has been done using crisp equivalence relations. In [2, 3, 7] we have made several innovations. We have studied fuzzy automata over a more general structure of truth values, over a complete residuated lattice, we have shown that better r...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are rev...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

In this paper, we introduce the notion of double-framed fuzzy quotient lattice in a fuzzy lattice and then some basic properties are investigated. Characterizations of double-framed fuzzy quotient lattices are given. Using a collection of lattices, a double framed fuzzy quotient lattice is established. The notion of fuzzy quotient lattice relation on the family of all I double-framed fuzzy sub ...

In this paper, the authors study the notion of n-fold implicative and fuzzy n-fold implicative filters, which correspond to various sets of provable formulaes, in BL-algebras. Several characterizations of fuzzy n-fold implicative filters are given and the authors analyse some relationships with various n-fold and fuzzy n-fold filters in BL-algebras, while constructing some algorithms for studyi...

the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as automata, labeled transition systems, Kripke models interpretations in description logics. Fuzzy bisimulations automata over a complete residuated lattice have been introduced by ?iri? et al. 2012. Logical characterizations (respectively, logics) the [0,1] with Gödel t-norm provided Fan 2015 Nguyen 202...