Related papers: Yoneda completeness and flat completeness of order…
A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-norms. This characterization will be useful in the study of topological and…
In the category \(\mathbf{V}\) of unital archimedean vector lattices, four notions of uniform completeness obtain. In all cases completeness requires the convergence of uniformly Cauchy sequences; the completions are distinguished by the…
We characterize Yoneda completeness for non-symmetric distances by combinations of metric and directed completeness. One of these generalizes the Kostanek-Waszkiewicz theorem on formal balls.
An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm…
The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…
The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to ${\sf Q}$-categories by Kostanek and Waszkiewicz. This paper concerns the influence of the structure of the quantale ${\sf Q}$ on the…
In this paper, we generalize the concept of unbounded norm (un) convergence: let $X$ be a normed lattice and $Y$ a vector lattice such that $X$ is an order dense ideal in $Y$; we say that a net $(y_\alpha)$ un-converges to $y$ in $Y$ with…
This paper presents a comparative study of three kinds of ideals in fuzzy order theory: forward Cauchy ideals (generated by forward Cauchy nets), flat ideals and irreducible ideals, including their role in connecting fuzzy order with fuzzy…
In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…
We prove a generic completeness result for a class of modal fixpoint logics corresponding to flat fragments of the two-way mu-calculus, extending earlier work by Santocanale and Venema. We observe that Santocanale and Venema's proof that…
Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX…
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…
We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially…
The notion of almost everywhere convergence has been generalized to vector lattices as unbounded order convergence, which proves a very useful tool in the theory of vector and Banach lattices. In this short note, we establish some new…
Let I be a dense linear order with a left endpoint but no right endpoint. We consider the lattice L(I) of finite unions of closed intervals of I. This lattice arises naturally in the setting of o-minimality, as these are precisely the…
Building on the notion of normed category as suggested by Lawvere, we introduce notions of Cauchy convergence and cocompleteness which differ from proposals in previous works. Key to our approach is to treat them consequentially as…
We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$-metric space to itself, the existence of a fixed point of $f$ is independent of the background model…
L.A.Zadeh introduced the concept of fuzzy set theory as the generalization of classical set theory in 1965 and further it has been generalized to intuitionistic fuzzy sets (IFSs) by Atanassov in 1983 to model information by the membership,…
The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found…
A net $(x_\alpha)$ in a vector lattice $X$ is said to be {unbounded order convergent} (or uo-convergent, for short) to $x\in X$ if the net $(\abs{x_\alpha-x}\wedge y)$ converges to 0 in order for all $y\in X_+$. In this paper, we study…