The aim of this paper is to promote web geometry and, especially, the Reidemeister closure condition as a powerful and intuitive tool characterizing associativity of the Archimedean triangular norms. In order to demonstrate its possible applications, we provide the full solution to the problem of convex combinations of nilpotent triangular norms. Keywords— Archimedean triangular norm, web geome...

The purpose of this paper is to discuss some categorical properties of probabilistic convergence spaces. Its main theses are: (1) the construct P-PrTop of probabilistic pretopological spaces is the extensional topological hull of the construct FTPcs of FT -diagonal probabilistic convergence spaces for every triangular norm T ; (2) the construct P-PsTop of probabilistic pseudotopological spaces ...

The issue of Cα-degree reduction of triangular Bézier surfaces is exposed. It is anticipated that both triangular Bézier surfaces are Cα-continuous at the vertices. The Euclidean norm as well as the L2−norm is used. The final solutions are given in terms of the matrix of degree raising, the Gram matrix, and the Bézier points. Moreover, it is shown that the solutions using both norms are equival...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

In this contribution we present some interesting constructions of non-continuous triangular norms. The first approach is based on strictly increasing sequences of natural numbers. An associative commutative monotone and bounded by minimum binary operation on these sequences induces a t-norm. The corresponding t-norm is left continuous and therefore it is applicable in the fuzzy logic. Several o...

The space of Lp graphons, symmetric measurable functions w:[0,1]2→R with finite p-norm, features heavily in the study sparse graph limit theory. We show that triangular cut operator Mχ—the sets all values a graphon below main diagonal unit square to 0—acting on this is not continuous respect norm. This achieved by showing as n→∞, norm truncation Tn matrices equipped grows infinity well. Due den...

Description Logics (DLs) are knowledge representation languages useful to represent concepts and roles. Fuzzy Description Logics (FDLs) incorporate both vague concepts and vague roles modeling them as fuzzy sets and fuzzy relations respectively. In the present paper, following ideas from Hájek, we propose the use of t-norm based (fuzzy) logics with truth constants in the language as logics unde...

Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An aarmative answer to the question whether in such logics a speciic level of satissability of a set of formulas can be characterized by the same level of satissability of its nite subsets is given. Tautologies, contradictions and contingencies with respect to such fuzzy logics are studied, in particular fo...