On the rules of intermediate logics

If the Visser rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of the Visser rules are admissible is not known. In this paper we give a brief overview of results on admissible rules in the context of intermediate logics. We apply these results to some well-known intermediate logics. We provide natural examples of logics for which the Visser rule are derivable, admissible but nonderivable, or not admissible. Supported by the Austrian Science Fund FWF under projects P16264 and P16539.     

Comparison of selection rules for ordinal optimization

The evaluation of performance of a design for complex discrete event systems through simulation is usually very time consuming. Optimizing the system performance becomes even more computationally infeasible. Ordinal optimization (OO) is a technique introduced to attack this difficulty in system design by looking at “order” in performances among designs instead of “value” and providing a probability guarantee for a good enough solution instead of the best for sure. The selection rule, known as the rule to decide which subset of designs to select as the OO solution, is a key step in applying the OO method. Pairwise elimination and round robin comparison are two selection rule examples. Many other selection rules are also frequently used in the ordinal optimization literature. To compare selection rules, we first identify some general facts about selection rules. Then we use regression functions to quantify the efficiency of a group of selection rules, including some frequently used rules. A procedure to predict good selection rules is proposed and verified by simulation and by examples. Selection rules that work well most of the time are recommended.     

A performance analysis of dispatching rules and a heuristic in static flowshops with missing operations of jobs

An experimental investigation of the performance of dispatching rules and a heuristic for scheduling in static flowshops with missing operations is undertaken in this study. The measure of performance is the minimization of total flow time of jobs. Permutation schedules are generated by using the heuristic for scheduling. General schedules, which can be permutation or non-permutation schedules, are obtained by using dispatching rules. Four dispatching rules, including a new dispatching rule, are considered. Two types of flowshops are studied: one with no missing operations of jobs and another with missing operations of jobs. In the latter type of flowshops, jobs with varying number of missing operations are considered. An extensive investigation of the performance of the dispatching rules and the heuristic is carried out. It is observed that the heuristic minimizes total flow time of jobs more than dispatching rules up to a certain level of missing operations of jobs in flowshops, after which dispatching rules perform better. The performance of the heuristic and the dispatching rules in terms of minimizing the makespan as a secondary measure is also reported.     

Combinatorial analysis of proofs in projective and affine geometry

The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates (i.e., solves the word problem). This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted to those known from the assumptions and cases. This “subterm property” is proved by permuting suitably the order of application of the geometric rules. As an example of the decision method, it is shown that there cannot exist a derivation of Euclid’s fifth postulate if the rule that corresponds to the uniqueness of the parallel line construction is taken away from the system of plane affine geometry.     

Equilibrium and effectiveness of two-parameter scoring rules

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.     

Calculus Rules for Derivatives of Multimaps

In this paper, by virtue of two intermediate derivative-like multifunctions, which depend on an element in the intermediate space, some exact calculus rules are obtained for calculating the derivatives of the composition of two set-valued maps. Similar rules are displayed for sums. Moreover, by using these calculus rules, the solution map of a parametrized variational inequality and the variations of the feasible set of a parametrized mathematical programming problem are studied. This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073).     

Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case error. A general algorithm is presented and explicit expressions for base 2 are given. To obtain an efficient component-by-component construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte Carlo rules based on higher order digital nets.     

On extrapolation of Jagerman and Stetter rules

In this paper quadrature rules introduced by Jagerman [1] and Stetter [2] are considered and asymptotic expansions for the error given. This allows to make use of the Romberg extrapolation process. Such rules can be viewed as generalizations of the well-known mid-point rule. Thus, numerical examples comparing these rules are finally presented.     

纵横步进编织规律的数学描述及其证明

对于纵横编织步进编织中的步长选取规律用精确的数学语言描述 ,并给出其严格的数学证明 ,为进一步设计和实现纵横编织技术提供了理论基础 .     

Evolution of fuzzy classifiers using genetic programming

In this paper, we propose a genetic programming (GP) based approach to evolve fuzzy rule based classifiers. For a c-class problem, a classifier consists of c trees. Each tree, T _i , of the multi-tree classifier represents a set of rules for class i. During the evolutionary process, the inaccurate/inactive rules of the initial set of rules are removed by a cleaning scheme. This allows good rules to sustain and that eventually determines the number of rules. In the beginning, our GP scheme uses a randomly selected subset of features and then evolves the features to be used in each rule. The initial rules are constructed using prototypes, which are generated randomly as well as by the fuzzy k-means (FKM) algorithm. Besides, experiments are conducted in three different ways: Using only randomly generated rules, using a mixture of randomly generated rules and FKM prototype based rules, and with exclusively FKM prototype based rules. The performance of the classifiers is comparable irrespective of the type of initial rules. This emphasizes the novelty of the proposed evolutionary scheme. In this context, we propose a new mutation operation to alter the rule parameters. The GP scheme optimizes the structure of rules as well as the parameters involved. The method is validated on six benchmark data sets and the performance of the proposed scheme is found to be satisfactory.     

Combinatorial analysis of proofs in projective and affine geometry

The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates (i.e., solves the word problem). This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted to those known from the assumptions and cases. This “subterm property” is proved by permuting suitably the order of application of the geometric rules. As an example of the decision method, it is shown that there cannot exist a derivation of Euclid’s fifth postulate if the rule that corresponds to the uniqueness of the parallel line construction is taken away from the system of plane affine geometry.     

An Investigation into the Decision Rules of Capital Investment Using Simulation

The paper explores the effectiveness of the major decision rules commonly applied to the selection of investment alternatives. The rules are applied to a continual stream of simulated investments, as they arise period by period throughout the planning horizon. Thus the dynamics of investing now rather than later, with capital rationing, are taken into account. The practitioners' preference for the payback period is examined for a typical series of simulated investments, and the returns are compared against the returns of the more academically acceptable discounting decision rules. Particular attention is devoted to the benefits of each of the decision rules with reference to both risk and average returns.     

On the selection of subdivision directions in interval branch-and-bound methods for global optimization

This paper investigates the influence of the interval subdivision selection rule on the convergence of interval branch-and-bound algorithms for global optimization. For the class of rules that allows convergence, we study the effects of the rules on a model algorithm with special list ordering. Four different rules are investigated in theory and in practice. A wide spectrum of test problems is used for numerical tests indicating that there are substantial differences between the rules with respect to the required CPU time, the number of function and derivative evaluations, and the necessary storage space. Two rules can provide considerable improvements in efficiency for our model algorithm.The work has been supported by the Grants OTKA 2879/1991, and MKM 414/1994.     

A SET OF SYMMETRIC QUADRATURE RULES ON TRIANGLES AND TETRAHEDRA

We present a program for computing symmetric quadrature rules on triangles and tetrahedra. A set of rules are obtained by using this program. Quadrature rules up to order 21 on triangles and up to order 14 on tetrahedra have been obtained which are useful for use in finite element computations. All rules presented here have positive weights with points lying within the integration domain.     

Analysis and design of sequencing rules for car sequencing

This paper presents novel approaches for generating sequencing rules for the car sequencing (CS) problem in cases of two and multiple processing times per station. The CS problem decides on the succession of different car models launched down a mixed-model assembly line. It aims to avoid work overloads at the stations of the line by applying so-called sequencing rules, which restrict the maximum occurrence of labor-intensive options in a subsequence of a certain length. Thus to successfully avoid work overloads, suitable sequencing rules are essential. The paper shows that the only existing rule generation approach leads to sequencing rules which misclassify feasible sequences. We present a novel procedure which overcomes this drawback by generating multiple sequencing rules. Then, it is shown how to apply both procedures in case of multiple processing times per station. For both cases analytical and empirical results are derived to compare classification quality.     

The design of simple subcontracting rules for make-to-order shops: An assessment by simulation

Subcontracting can be an important means of overcoming capacity shortages and of workload balancing, especially in make-to-order companies characterized by high variety, high demand variation and a job shop configuration. But there is a lack of simple, yet powerful subcontracting rules suitable for such contexts. The few existing rules were developed for single work center shops and neglect the actual subcontracting lead time, meaning some subcontracted jobs are destined to become tardy. This study uses Workload Control theory on matching required and available capacity over time to propose four new rules that address these shortcomings. The new rules are compared against four existing rules using an assembly job shop simulation model where the final, assembled product consists of several sub-assemblies that either flow through an internal job shop or are subcontracted. The best new rules stabilize the direct load queuing in front of a work center and significantly improve performance compared to the existing rules. For example, when the workload exceeds capacity by 10%, a 50% reduction in percentage tardy can be achieved. By examining how the workload behaves over time, we reveal that improvements come from selectively subcontracting the sub-assemblies that would otherwise cause overloads, thereby cutting off peaks in the workload.     

Pareto分布参数的经验Bayes检验的收敛速度:NA样本情形

本文讨论了NA(negativeassociation)样本情形Pareto分布参数的经验Bayes(EB)单侧和双侧检验问题.利用概率密度函数的核估计构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性并获得了其收敛速度.     

The Construction of Reducible Quadrature Rules for Volterra Integral and Integro-differential Equations

A formal relationship between quadrature rules and linear multistepmethods for ordinary differential equations is exploited forthe generation of quadrature weights. Employing the quadraturerules constructed in this way, step-by-step methods for secondkind Volterra integral equations and integro-differential equationsare defined and convergence and stability results are presented. The construction of the quadrature rules generated by the backwarddifferentiation formulae is discussed in detail. The use ofthese rules for the solution of Volterra type equations is proposedand their good performance is demonstrated by numerical experiments.     

Knowledge representation and acquisition in expert systems for pattern recognition

A new approach to the design of fuzzy expert systems is proposed. The representation of knowledge and the formation of statements by fuzzy logic tools are discussed in detail. A model of fuzzy inference is described. Primary attention is given to automatic extraction of knowledge (fuzzy inference rules) from a set of precedents. Various performance criteria for rules are introduced, and an algorithm for their generation (the method of effective restrictions) is proposed. An extension of the type of admissible rules by introducing a fuzzy disjunction operation is described. The possibility of optimizing the rules found is explored. The benefits of the approaches proposed are illustrated by experiments.