in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

As it is well-known, Lukasiewicz developed in [2] the many-valued propositional calculi based on two primitive connectives, negation N and implication C, which were defined semantically. Complete axiomatizations followed later on. Among the works on this argument, we mention Wajsberg [9], Rosser and Turquette [8], Mc Naughton [3], Rose and Rosser [7], Meredith [4], Chang [1], Rose [5], [6]. It ...

If logic programs are interpreted over a three-valued logic, then often Kleene’s strong three-valued logic with complete equivalence and Fitting’s associated immediate consequence operator is used. However, in such a logic the least fixed point of the Fitting operator is not necessarily a model for the program under consideration. Moreover, the model intersection property does not hold. In this...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

Similarity: measure of how close to each other two instances are. The “closer” the instances are to each other, the larger is the similarity value. Dissimilarity: measure of how different two instances are. Dissimilarity is large when instances are very different and is small when they are close. Proximity: refers to either similarity or dissimilarity Distance metric: a measure of dissimilarity...

This paper presents some linear adaptive non-nested multigrid methods which are applied to linear elastic problems discretized with triangular and tetrahedral nite elements using unstructured and Delaunay mesh generators. The Zienkiewicz-Zhu error estimator and a h-re nement procedure are used to obtain the non-nested meshes used by the multigrid methods. We solve problems with a speci ed perce...

Applications of mesh adaption techniques could be found in the numerical solution of PDE’s or in the optimal triangulation of surfaces for shape representation or graphic display. The scope of this work is to verify through numerical experiments the effectiveness of some algorithms for the control of the L∞ error norm for piece–wise linear approximation on 2D unstructured triangular meshes. The...

Abstract. Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on triangular meshes and their Voronoi duals. On a two-dimensional convex polygonal domain, it is shown that a suitable combination of the solutions of these two schemes converges with second-order accuracy towards the exact solution in the L n...

The optimal robust disturbance rejection problem plays an important role in feedback control theory. Here its time-varying version is solved explicitly in terms of duality and operator theory. In particular, the optimum is shown to satisfy a time-varying allpass property. Moreover, optimal performance is given in terms of the norm of a bilinear form. The latter depends on a lower triangular pro...

A uniform bound of the 1−norm is given for the inverse of lower triangular Toeplitz matrices with nonnegative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brun-ner concerning the convergence of the one-point collocation method for the Abel's...