in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

Presented is a reduction of fuzzy Galois connections and fuzzy concept lattices to (crisp) Galois connections and concept lattices: each fuzzy concept lattice can be viewed as a concept lattice (in a natural way). As a result, a simple proof of the characterization theorem for fuzzy concept lattices is obtained. The reduction enables us to apply the results worked out for concept lattices to fu...

In the framework of fuzzy algebras with fuzzy equalities and acomplete lattice as a structure of membership values, we investigate fuzzyequational classes. They consist of special fuzzy algebras fullling the samefuzzy identities, dened with respect to fuzzy equalities. We introduce basicnotions and the corresponding operators of universal algebra: construction offuzzy subalgebras, homomorphisms...

In this paper we define a correspondence between the set of all fuzzy hideals of a Γ-hemiring S and the set of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. We deduce that the lattice of all fuzzy hideals of a Γ-hemiring is isomorphic to the lattice of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. Finally, the cartesian product of corresponding fuzzy h-idea...

Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT 1 The paper presents results on factorization by similarity of fuzzy concept lattices with hedges. A fuzzy concept lattice is a hierarchically ordered collection of clusters extracted from tabular data. The basic idea of factorization by similarity is to have, instead of a possibly large original fuzzy concep...

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy vers...

Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s Kα operators allow us to retrieve the information given by the transition functions of...

Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neu...

In this paper, we introduced two types of fuzzy stabilizers St R (F) and St ⊕ R (F) of a fuzzy set F and the stabilizer St ∨(F, G) of F with respect to G in IMTL-algebras. We proved that St R (F), St ⊕ R (F) and St ∨(F, G) are fuzzy filters of M. We investigated some properties of the stabilizers. By introducing the ⊗̃ operation of two fuzzy filters, we prove that ⊗̃ and St∨(·, ·) form an adjoint...