Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more e1ective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input...

ClassSm variable transformationswith integerm for finite-range integrals were introduced by the author (Numerical Integration IV, International series of Numerical Mathematics, Basel, 1993, pp. 359–373) about a decade ago. These transformations “periodize” the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even m. In a recent work b...

Quadrupole mass filters (QMFs) are usually not used to analyze high m/z ions, due to the low frequency resonant circuit that is required to drive them. Here we describe a new approach to generating waveforms for QMFs. Instead of scanning the amplitude of a sine wave to measure the m/z spectrum, the frequency of a trapezoidal wave is digitally scanned. A synchronous, narrow-range (<0.2%) amplitu...

The paper deals with the trapezoidal rule discretization of a class of linear delay differential equations, with a special emphasis on equations with a proportional delay. Our purpose is to analyse the asymptotic properties of the numerical solutions and formulate their upper bounds. We also survey the known results and show that our formulae improve and generalize these results. In particular,...

Are Plurality voting, the Kemeny rule, Approval voting, and the Borda Mean Dichotomy rule all versions of the same voting rule? Yes, in a sense. In an extension of work by Barthélemy and Monjardet [3], we consider functions F that assign real number scoring weights F (R1, R2) to pairs of binary relations on a finite set A of alternatives, serving as symmetric measures of similarity between R1 a...

Aspects of continuous and discrete harmonic analysis on the circle are generalized to star graphs, and through spherical coordinates to the two sphere. The resulting function theory is used to analyze trapezoidal rule integration on the two sphere. 2000 Mathematics Subject Classification 65D30, 65T99, 34B45

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

We introduce a tractable multi-issue model of electoral competition in which candidates are exogenously committed to particular positions on a subset of issues, while they can choose a sequence of binary positions for the remaining issues to maximize their winning probability. A majorityefficient position is defined as one where a candidate cannot make a majority of the electorate better off, t...

AUC is an important parameter in pharmacokinetic studies. There are different ways to calculate AUC. Sometime, the statistician or pharmacokineticist has to choose one particular method to calculate AUC depending on the actual concentration data. Among many pharmacokinetic approaches and modeling analyses, traditional trapezoidal, log-linear trapezoidal, Lagrange polynomial integration, and Pur...