In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$  the set of all real numbers. A great many standard mappings on algebr...

The approximation numbers of Hardy–type operators on trees. Abstract The Hardy operator Ta on a tree Γ is defined by (Taf)(x) := v(x) x a u(t)f (t)dt for a, x ∈ Γ. Properties of Ta as a map from L p (Γ) into itself are established for 1 ≤ p ≤ ∞. The main result is that, with appropriate assumptions on u and v, the approximation numbers an(Ta) of Ta satisfy (*) lim n→∞ nan(Ta) = αp Γ |uv|dt for ...

Abstract In this paper we investigate upper and lower bounds of the norms of the circulant matrices whose elements are k−Jacobsthal numbers and k−Jacobsthal Lucas numbers.

In this paper we propose a new method for ranking Z- numbers and generalizations. This method is based on the internal structure of the artificial neural network, which suggests that the structure of this network consists of inputs weights and the transfer function linear, nonlinear and sometimes linear and nonlinear. It is shown that the proposed method while possessing the ranking properties ...

The multiobjective two person matrix game problem with fuzzy payoffs is considered in this paper. It is assumed that fuzzy payoffs are triangular fuzzy numbers. The problem is converted to several multiobjective matrix game problems with interval payoffs by using the $alpha$-cuts of fuzzy payoffs. By solving these problems some $alpha$-Pareto optimal strategies with some interval outcomes are o...