We study the behavior of rules for the adjudication of conflicting claims when there are a large number of claimants with small claims. We model such situations by replicating some basic problem. We show that under replication, the random arrival rule (O’Neill, 1982) behaves like the proportional rule, the rule that is the most often recommended in this context. Also, under replication, the min...

A “scoring rule” is an assignment of a value to every tuple (of varying sizes). This paper is concerned with the issue of how to modify a scoring rule to apply to the case where weights are assigned to the importance of each argument. We give an explicit formula for incorporating weights that can be applied no matter what the underlying scoring rule is. The formula is surprisingly simple, in th...

The effects of cutting edge shapes on the phenomena of rubbing and ploughing in nano-abrasive machining were investigated. The shapes under investigation include flat, spherical and trapezoidal shapes. The tool with the flat end geometry shows a fast initiation of ploughing, because it has the largest surface area to engage more atoms. It doesn’t show rubbing phenomenon at the (initial) depth o...

The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule.

A generalized trapezoid rule is derived. Various error bounds for this rule are established. © 2005 Elsevier Ltd. All rights reserved. MSC: 26D15; 65D30

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims on some amount of a scarce resource, but also by some exogenous ex-ante conditions (characteristics), different from claims (e.g., endowments, entitlements, wealth, obligations, assets). Inequalities in the ex-ante conditions induce compensations between agents which influence t...

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...

The variance of fuzzy random variables often appears in fuzzy random programming problems. Based on the definition of the variance of a fuzzy random variable, this paper attempts to deduce several formulas for the variances of trapezoidal fuzzy random variables, in which the randomness is characterized by uniform distribution. Firstly, we give the moment formulas for trapezoidal fuzzy variables...

This paper covers two aspects of microstrip antenna design. The first is the analysis of trapezoidal patch microstrip antenna with V-shaped slot which operate at the centre frequency of 5.5 GHz. The second aspects are the analysis and design of inverted V-shaped slot cut trapezoidal microstrip antenna operates at centre frequency of 4.1 GHz. The simulation has been done through IE3D simulator. ...