The expected value models on Sugeno measure space

Uncertain programming is a theoretical tool to handle optimization problems under uncertain environment. The research reported so far is mainly concerned with probability, possibility, or credibility measure spaces. Up to now, uncertain programming realized in Sugeno measure space has not been investigated. The first type of uncertain programming considered in this study and referred to as an expected value model optimizes a given expected objective function subject to some expected constraints. We start with a concept of the Sugeno measure space. We revisit some main properties of the Sugeno measure and elaborate on the g_λ random variable and its characterization. Furthermore, the laws of the large numbers are discussed based on this space. In the sequel we introduce a Sugeno expected value model (SEVM). In order to construct an approximate solution to the complex SEVM, the ideas of a Sugeno random number generation and a Sugeno simulation are presented along with a hybrid approach.     

Multicriteria Goal Games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.     

Price Expectations and Cobwebs Under Uncertainty

Classical approaches to location problems are based on the minimization of the average distance (the median concept) or the minimization of the maximum distance (the center concept) to the service facilities. The median solution concept is primarily concerned with the spatial efficiency while the center concept is focused on the spatial equity. The k-centrum model unifies both the concepts by minimization of the sum of the k largest distances. In this paper we investigate a solution concept of the conditional median which is a generalization of the k-centrum concept taking into account the portion of demand related to the largest distances. Namely, for a specified portion (quantile) of demand we take into account the entire group of the corresponding largest distances and we minimize their average. It is shown that such an objective, similar to the standard minimax, may be modeled with a number of simple linear inequalities. Equitable properties of the solution concept are examined.     

Yokes and tensors derived from yokes

A yoke on a differentiable manifold M gives rise to a whole family of derivative strings. Various elemental properties of a yoke are discussed in terms of these strings. In particular, using the concept of intertwining from the theory of derivative strings it is shown that a yoke induces a family of tensors on M. Finally, the expected and observed -geometries of a statistical model and related tensors are shown to be derivable from particular yokes.     

Stabilization through taxation inn-person games

In formulating solutions forn-person cooperative games, the concept of stability has played a dominant role. Although the core concept has the strongest stability, the core of a game is often empty. In this paper, the taxation system is incorporated into our framework, so that a modified solution concept, which enjoys the stability of core, can be developed. Various formulations based on principles such astaxation proportional to income andequity after tax are given.     

Index Sets in Modeling Languages

Index sets are an integral and fundamental part of every mathematical modeling language. They assist the modeler in grouping various objects and entities. Index sets are also used extensively in the mathematical notation to write an expression in a concise way. An example is the sigma notation for formulating the summation of an unknown number n of terms. In this paper, the concept of index set is introduced in the context of modeling languages. The main objective is to propose an extension and generalization of the concept of index sets, which is the concept of hierarchical index sets. The paper concludes with an application, which clearly shows the usefulness of this concept.     

Weighted Euclidean centers

This article addresses the derivation of a Euclidean center, which is defined as the point in decision space from which one can inscribe the largest sphere contained by the constraints. We extend this concept by introducing its weighted version, which we term the weighted Euclidean center. We show that by assigning weights to the different decision variables we can traverse the entire decision space. In addition, we show that the concept of a weighted Euclidean center and that of the achievement scalarizing function introduced by Wierzbicki are intimately related.     

A hierarchical location-allocation model with travel based on expected referral distances

The hierarchical p-median location-allocation model assumes that patrons always travel to the closest facility of appropriate level and that their interests are best served when the distances they must travel to do this are minimized. This assumption about travel behavior is unrealistic, patrons in the real world are known, for instance, to bypass lower level facilities that can serve their needs to attend higher level facilities. We introduce the concept of “expected distance under referral” to deal with such irrationality and incorporate it into a location-allocation model that minimizes the negative effects of such irrational behavior. We demonstrate the model with several types of non-optimal travel behavior.     

Mean-variance Hedging for Pricing European-type Contingent Claims with Transaction Costs

In this paper,a European-type contingent claim pricing problem with transaction costs is considered by a mean-variance hedging argument.The investor has to pay transaction costs which areproportional to the amount of stock transacted.The writer‘‘s hedging object is to minimize the hedgingrisk,defined as the variance of hedging error at expiration,with a proper expected excess return level.At first, we consider the mean-variance hedging problem:for initial hedging wealth f,maximizing the excess expected return under the minimum hedging risk level V0.On the other hand,we consider a mean-variance portfolio problem,which is to maximize the expected return with initial wealth 0 under the same risk level V0.The minimum initial hedging wealth f,which can offset the difference of the maximum expected return of these two problems,is the writer‘s price.     

Representing triangulated graphs in stars

A graphG is calledrepresentable in a tree T, ifG is isomorphic to the intersection graph of a family of subtrees ofT. In this paper those graphs are characterized which are representable in some subdivision of theK _1,n. In the finite case polynomial-time recognition algorithms of these graphs are given. But this concept can be generalized to essentially infinite graphs by using no more trees but ‘tree-like’ posets and representability of graphs in these posets.     

Incidence matrices and inequalities for combinatorial designs

In this paper we use incidence matrices of block designs and row–column designs to obtain combinatorial inequalities. We introduce the concept of nearly orthogonal Latin squares by modifying the usual definition of orthogonal Latin squares. This concept opens up interesting combinatorial problems and is expected to be useful in planning experiments by statisticians. © 2002 John Wiley & Sons, Inc. J Combin Designs 10: 17–26, 2002     

Statistical Causality,Extremal Measures and Weak Solutions of Stochastic Differential Equations with Driving Semimartingales

In this paper we consider different concepts of causality in filtered probability spaces. Especially, we consider a generalization of a causality relationship “G is a cause of J within H ” which was first given by Mykland (1986) and which is based on Granger’s definition of causality (Granger, Econometrica 37:424–438, 1969). Then we apply this concept on weak solutions of stochastic differential equations with driving semimartingales. We also show that the given causality concept is closely connected to the concept of extremality of measures and links Granger’s causality with the concept of adapted distribution. Finally, the concept of causality is applied on solution of martingale problem.     

Optimal pension fund management under multi-period risk minimization

In this paper, a multi-period stochastic optimization model for solving a problem of optimal selection of a pension fund by a pension plan member is presented. In our model, members of the pension plan are given a possibility to switch periodically between J types of funds with different risk profiles and so actively manage their risk exposure and expected return. Minimization of a multi-period average value-at-risk deviation measure under expected return constraint leads to a large-scale linear program. A theoretical framework and a solution for the case of the pension system of Slovak Republic are presented.     

Probabilisticl p distances in location models

Modelling distances with thel _p norm is very widespread in site selecting location problems. This paper deals with the concept of a probabilisticp parameter which permits uncertainty in the directness of the routes that can be taken between a facility and demand points. This paper establishes the rather surprising result that the expected distances can themselves be closely approximated byl _p distances with appropriately chosenp parameters. This result is very useful when, as is often the case, expected distances are used in the optimization criterion.     

Prediction error criterion for selecting variables in a linear regression model

Several criteria, such as CV, C _p , AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C _p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error R _PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper, we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R _PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore, using simulations, we examine some peculiarities of all these criteria.     

A periodical replacement model based on cumulative repair‐cost limit

This paper considers a periodical replacement model based on a cumulative repair‐cost limit, whose concept uses the information of all repair costs to decide whether the system is repaired or replaced. The failures of the system can be divided into two types. One is minor failure that is assumed to be corrected by minimal repair, while the other is serious failure where the system is damaged completely. When a minor failure occurs, the corresponding repair cost is evaluated and minimal repair is then executed if this accumulated repair cost is less than a pre‐determined limit L, otherwise, the system is replaced by a new one. The system is also replaced at scheduled time T or at serious failure. Long‐run expected cost per unit time is formulated and the optimal period T* minimizing that cost is also verified to be finite and unique under some specific conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

Railway scheduling reduces the expected project makespan over roadrunner scheduling in a multi-mode project scheduling environment

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (Critical chain, 1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.     

On random cartesian trees

Cartesian trees are binary search trees in which the nodes exhibit the heap property according to a second (priority) key. If the search key and the priority key are independent, and the trees is built based on n independent copies, Cartesian trees basically behave like ordinary random binary search trees. In this article, we analyze the expected behavior when the keys are dependent: in most cases, the expected search, insertion, and deletion times are Φ(√n). We indicate how these results can be used in the analysis of divide-and-conguer algorithms for maximal vectors and convex hulls. Finally, we look at distributions for which the expected time per operation grows like n^a for a ?[1/2, 1]. © 1994 John Wiley & Sons, Inc.     

Projective mappings between projective lattice geometries

The concept of projective lattice geometry generalizes the classical synthetic concept of projective geometry, including projective geometry of modules.In this article we introduce and investigate certain structure preserving mappings between projective lattice geometries. Examples of these so-calledprojective mappings are given by isomorphisms and projections; furthermore all linear mappings between modules induce projective mappings between the corresponding projective geometries.