The nth partial sums of a classical Fourier series have large oscillations near the jump discontinuities. This behaviour is the well-known Gibbs phenomenon. Recently, the inverse polynomial reconstruction method (IPRM) has been successfully implemented to reconstruct piecewise smooth functions by reducing the effects of the Gibbs phenomenon for Fourier series. This paper addresses the 2-D fractional Fourier series (FrFS) using the same approach used with the 1-D fractional Fourier series and finds that the Gibbs phenomenon will be observed in 1-D and 2-D fractional Fourier series expansions for functions at a jump discontinuity. The existing IPRM for resolution of the Gibbs phenomenon for 1-D and 2-D FrFS appears to be the same as that used for Fourier series. The proof of convergence provides theoretical basis for both 1-D and 2-D IPRM to remove Gibbs phenomenon. Several numerical examples are investigated. The results indicate that the IPRM method completely eliminates the Gibbs phenomenon and gives exact reconstruction results.

This paper describes two methods to construct fuzzy inference rules by the simplified fuzzy reasoning. The present methods have a construction mechanism of the rule unit that is applicable in two parameters: the central value and the width of the membership function in the antecedent part. The first approach is to create a rule unit near the selected rule which has the nearest position from the central input space for the central value. The second is to create a rule unit near the selected rule which has the minimum width for the width. Experimental results are presented in order to show that the proposed methods are effective in difference on the inference error and the number of learning iterations.

A large-scale primarily public system requires in addition to high reliability, a broad range of applications from control to information services. As construction is phased-in this system must be flexible, changeable and able to grows as the needs arise. However, a changing a system may lead to loss of reliability. A system that is able to change and grow in a reliable and stable manner is called an assurance system and the technology it uses is called assurance technology. This paper describes the basic technology, phased-in system construction and so on of assurance technology based on an autonomous decentralized system. It further discusses application of assurance technology to ATOS as an example of a large-scale transport operation control system. Note: ATOS; Autonomous Decentralized Transport Operation Control System