$G_{\delta }$-separation axioms are introduced in ordered fuzzy topological spaces and some of their basic properties are investigated besides establishing an analogue of Urysohn’s lemma.

We analyze the existence of fuzzy sets of a universe that are convex with respect to certain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping $F:[0,1]\times [0,1]\to [0,1]$, a fuzzy subset, say $X$, of the real line is said to be $F$-convex if for any $x,y,z\in ℝ$ such that $x\le y\le z$, it holds that ${\mu }_X\left(y\right)\ge F({\mu }_X\left(x\right),{\mu }_X\left(z\right))$, where ${\mu }_X:ℝ\to [0,1]$ stands here for the membership function...

In a previous work ([3]) we proved that the Nguyen's condition for [f(tilde-A)]α to be equal to f(Aα) also holds for the most general class of the L-fuzzy subsets, where L is an arbitrary lattice. Here we recall the main points of the proof ad present some examples ralated to non-linear lattices.

An overview of generated triangular norms and their applications is presented. Several properties of generated $t$-norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.

In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.

In this paper we study two ways of generating multi-dimensional aggregation functions. First of all we obtain multi-dimensional OWA operators in two different ways, one of them through quantifiers and the other through sequences. In the first case, we see that all the operators we obtain are multi-dimensional aggregation functions. We then characterize the multi-dimensional aggregation functions that are generated by quantifiers. In the second case, we characterize the sequences that provide multi-dimensional...

The basic tool considered in this paper is the so-called graded set, defined on the analogy of the family of α-cuts of a fuzzy set. It is also considered the corresponding extensions of the concepts of a point and of a real number (again on the analogy of the fuzzy case). These new graded concepts avoid the disadvantages pointed out by Gerla (for the fuzzy points) and by Kaleva and Seikkala (for the convergence of sequences of fuzzy numbers).