in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...

Some applications use data formats (for example STL file format), where a set of triangles is used to represent a surface of an object and it is necessary to reconstruct the regular triangular mesh from such a data format for many applications. It is a lengthy process for large data sets as the time complexity of this process is O(N) or O(N lgN), where N is a number of triangles. Hash data stru...

The main purposes of this paper are to probe for the entropy differences between arithmetically manipulated Triangular Fuzzy Numbers (TFNs) using Shannon’s Function; and to study the relationships between any two TFNs. Simultaneously, we expand on the articles of Wang et al. [6] and Wang et al. [5]. The entropy differences between two TFNs subjected to different arithmetic operations are classi...

In this paper, a so-called Plateau-Mesh problem is proposed, that is, to find a triangular mesh with the boundary formed by a given spacial closed polygon, whose area is minimum among all triangular meshes with the same boundary. To solve this problem, the former work by minimizing a function describing the mesh area directly, cannot obtain the global minimum of the function, only obtain its lo...

This paper proposes an efficient algorithm for simultaneous reduction of three matrices. The algorithm is a blocked version of the algorithm described by Miminis and Page (1982) which reduces A to the m-Hessenberg form, and B and E to the triangular form. The m-Hessenberg– triangular–triangular form of matrices A, B and E is specially suitable for solving multiple shifted systems. Such shifted ...

A new triangular "finite element" is described; it involves the 12-parameter family of all quartic polynomial functions that are "tricubic" in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a continuously differentiable function, tricubic on ea...

This article introduces a new application of piecewise linear orthogonal triangular functions to solve fractional order differential-algebraic equations. The generalized triangular function operational matrices for approximating Riemann-Liouville fractional order integral in the triangular function (TF) domain are derived. Error analysis is carried out to estimate the upper bound of absolute er...