In this paper, a numerical approach based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of Fredholm integral equations of the first kind. By using the orthogonal triangular functions as a basis in Galerkin method, the solution of linear integral equations reduces to a system of algebric equations. If the recent system become ill-conditioned...

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product trian...

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...

The Partial-Element-Equivalent-Circuit (PEEC) approach is an effective method to convert three-dimensional on-chip multiconductor structures to circuit-level descriptions. In this paper, a triangular-mesh-based PEEC approach is described, wherein the surfaces of arbitrarily-shaped conducting structures are represented by triangular mesh tesselations. A coupled EM-circuit formulation is obtained...

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, w...

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum infere...

A simulator is presented for computing the interconnect capacitances of ICs and PCBs using Green's functions. The capacitance simulator forms part of a simulation program [1] for a complete signal analysis of PCBs and ICs. The tool is suitable for computing discrete and coupling capacitances of arbitrary geometries. The model approximates the charge density of the conductors by dividing the sur...

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This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work be...

The paper presents a new closed-form expression for the fractional Fourier transform of generalized Triangular and Welch window functions. Fractional Fourier Transform (FrFT) is a parameterized transform having an adjustable transform parameter which makes it more flexible and superior over ordinary Fourier transform in several applications. It is an important tool used in signal processing for...