Schnyder characterized planar graphs in terms of order dimension. This seminal result found several extensions. A particularly far reaching extension is the Brightwell-Trotter Theorem about planar maps. It states that the order dimension of the incidence poset PM of vertices, edges and faces of a planar map M has dimension at most 4. The original proof generalizes the machinery of Schnyder-path...

The aim of this paper is to study monadic L-fuzzy quantifiers of the type 〈1〉 determined by fuzzy measures. These fuzzy quantifiers are defined using a novel notion of ⊗-fuzzy integral. Several semantic properties of these L-fuzzy quantifiers are studied. Keywords— fuzzy integral, fuzzy logic, fuzzy measure, fuzzy quantifier, generalized quantifier

We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones propose...

In this paper the concept of bi-conjugative relations on sets is introduced. Characterizations of this relations are obtained. In addition, particulary we show that the anti-order relation in poset (L,6) is not a bi-conjugative relation. Mathematics Subject Classification (2010): Primary 03E02, 06A11; Secondary 20M20

The concept of L-fuzzy lattice is presented by means of an L-fuzzy partially ordered set. An L-fuzzy partially ordered set A is an L-fuzzy lattice if and only if one of A[a], A([a]), and A(a) is a lattice.

The aim of this paper is to study the concept of Intuitionistic L-fuzzy subrings and Intuitionistic L-fuzzy ideals of a ring R. In this direction definitions and properties relating to Intuitionistic L-fuzzy subrings of R and Intuitionistic L-fuzzy ideals of R are introduced and discussed. We introduce a special type of Quotient ring.

In this paper, we introduce the notions of L-fuzzy quasi-uniformities and Lfuzzy interior operators in complete residuated lattices. We investigate the L-fuzzy quasiuniformities induced by L-fuzzy interior operators. We study the relationships between Lfuzzy interior operators and L-fuzzy quasi-uniformities. We give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54F05

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.