We study the problem: if ãi, i ∈ N are fuzzy numbers of triangular form, then what is the membership function of the infinite (or finite) sum ã1+ã2+· · · (defined via the sup-product-norm convolution)?

Given a triangular Bézier surface of degree n, the problem of multi-degree reduction by a triangular Bézier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order α. The l2and L2-norm combined with the constrained least-squares me...

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...

For a quantale I, which is unit interval endowed with continuous triangular norm and the Barr extension β¯I of ultrafilter monad to I-Rel, characterization discrete presheaf associated given. It also proved that, when & Łucasiewicz norm, isomorphic saturated prefilter monad, product prime functional ideal submonad monad.

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

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 ...

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

Triangular norms are a generalisation of the classical two-valued conjunction. They were originally introduced for definition of the probabilistic (statistical) metric spaces as a generalisation of the classical triangle inequality for ordinary metric spaces. The next investigations were related with axiomatic of these norms. In this paper, a new t-norm is proposed which is generalisation of th...

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...

Stability results are proved for traveling waves in a class of reaction-diffusion systems that arise in chemical reaction models. The class includes systems in which there is no diffusion in some equations. A weight function that decays exponentially at one end is required to stabilize the essential spectrum. Perturbations of the wave in H1 or BUC that are small in both the weighted norm and th...