Path algebras are additively idempotent semirings and generalize Boolean algebras, fuzzy algebras, distributive lattices and inclines. Thus the Boolean matrices, the fuzzy matrices, the lattice matrices and the incline matrices are prototypical examples of matrices over path algebras. In this paper, generalized fuzzy matrices are considered as matrices over path algebras. Compositions of genera...

An L-fuzzy context is a triple consisting of a set of objects, a set of attributes and an L-fuzzy binary relation between them. An l-cut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater or equal than l. Proto-fuzzy concept is a triple made of a set of objects and a set of attributes, which form a con...

The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve ma...

This paper proposes two hierarchical schemes for learning, one for clustering and the other for classification problems. Both schemes can be implemented on a fuzzy lattice neural network (FLNN) architecture, to be introduced herein. The corresponding two learning models draw on adaptive resonance theory (ART) and min-max neurocomputing principles but their application domain is a mathematical l...

B. Ganter, R. Wille initiated formal concept analysis, concept lattice is one of the main notions and tools, see [12]. Some researchers have investigated the fuzzification of the classical crisp concept lattice. In [1], from the point of view of fuzzy logic, R. Bĕlohlávek investigated concept lattice in fuzzy setting. In [16, 17], S. Krajči studied generalized concept lattice. On the other hand...

Our aim in this paper is to introduce and study a new sort of fuzzy sublattice (ideal, filter) of a lattice called ) q , ( ∨ ∈ ∈ -fuzzy sublattice (ideal, filter). These fuzzy sublattices (ideals, filters) are characterized by their level sublattices (ideals, filters). Finally, we give a generalization of ) q , ( ∨ ∈ ∈ -fuzzy sublattices (ideals, filters).

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of Gfuzzy congruences on semigroups.

Vagueness and high dimensional space data are usual features of current data. The paper is an approach to identify conceptual structures among fuzzy three dimensional data sets in order to get conceptual hierarchy. We propose a fuzzy extension of the Galois connections that allows to demonstrate an isomorphism theorem between fuzzy sets closures which is the basis for generating lattices ordere...

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considere...

Contrasting to Description Logics (DLs), there are some inherent shortcomings in classical fuzzy Description Logics (FDLs). For example, they no longer satisfy the complementary laws. In this paper, to analyze these shortcomings derived from Zadeh semantics, an improved fuzzy set definition using Boolean lattices is approached, whereas, the analogous definition of Zadeh Fuzzy Set can only use a...