The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.

In this paper we summarize our results obtained recently on continuous triangular norms that are migrative with respect to an arbitrary continuous triangular norm. We start with the original notion of migrativity and completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent t-norm classes, the characterization and construc...

In this paper, we give upper and lower bounds for the spectral norms of circulant matrices A n = Circ(F n−1) and B n = Circ(L (k,h) n and L (k,h) n are the (k, h)-Fibonacci and (k, h)-Lucas numbers, then we obtain some bounds for the spectral norms of Kronecker and Hadamard products of these matrices.

We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products.

This paper deals with triangular norms and conorms defined on the extended set N of natural numbers ordered by divisibility. From the fundamental theorem of arithmetic, N can be identified with a lattice of functions from the set of primes to the complete chain {0, 1, 2, ...,+∞}, thus our knowledge about (divisible) t-norms on this chain can be applied to the study of t-norms on N. A characteri...

In this article we are presenting two new classes of t-norm and t-conorm based generalized means with weights. We are going to test usability of these measures which we get by combining classes of t-norms and t-conorms to the generalized mean operator. Since we are using the generalized mean we have an additional parameter that controls the power which the argument values are raised. Dombi and ...

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 initially high performance of a socioeconomic organization is quite often subject to gradual erosion over time. We present a simple model which captures such a phenomenon. We assume that players are partly motivated by certain psychological factors, norms and morale, and they are willing to exert extra effort if others do so. This results in a ”continuum” of equilibrium effort levels, whose...

In this paper we provide a simple characterization of the dominance in two classes of continuous triangular norms. In particular, we solve the dominance of (i) ordinal sum t-norms that use the Łukasiewicz t-norm as the only summand operation and (ii) ordinal sum t-norms that use the product t-norm as the only summand operation. In both cases, the dominance relation is characterized by a simple ...