An inexact-stochastic dual water supply programming model

This paper introduces an inexact-stochastic dual water supply programming (ISDWSP) model based on analysis of the inexact characteristics in demand and supply subsystems of dual water supply system and their dynamic interactions. The model is based on an inexact chance-constrained programming (ICCP) method allowing both distribution information in B (right parameter in the model constrain) and uncertainties in A (left parameter in the model constrain) and C (parameter in the model function) with objective of maximizing economic return, and constrained to available water resource, economical, environmental and social constrains. The decision-making variables of ISDWSP model are water demanded amount by different sectors and waterworks building scale. In the solution process, the ISDWSP is transformed into two deterministic sub-models, which correspond to the upper and lower bounds of the objective function, and the reasonable interval solution set in the given decision space can be obtained by solving the two sub-models. Thus, decision alternatives can be obtained by adjusting decision variable values within their solution intervals and will be useful for decision makers to choose the projected applicable conditions considering tradeoffs between eco-environmental and economic objectives. The model is also applied in a new developing zone of North China with the results of the case study providing reasonable solutions for dynamic planning of different source water (DSW) allocation in a regional system. Finally, waterworks building plan is generated based on the projected applicable conditions.     

Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics R^a based on power divergence. All R^a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R^a under local alternatives. We obtain an expression of approximation for the distribution of R^a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R^a. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R^a. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.     

Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions

We present a new method, called UTA^GMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A^R ⊆ A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA^GMS method is intended to be used interactively, with an increasing subset A^R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA^GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA^GMS software. Some extensions of the method are also presented.     

Enhanced-interval linear programming

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A^±, B^± and C^±) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to that of interval linear programming (ILP), which helps to achieve insight into the expected-value-oriented trade-off between system benefits and risks of constraint violations. The degree of uncertainty of its enhanced-interval objective function (EIOF) would be lower than that of ILP model when the solution space is absolutely feasible, and the EIOF’s expected value could be used as a criterion for generating the appropriate alternatives, which help decision-makers obtain non-extreme decisions. Moreover, because it can be decomposed into two submodels, EILP’s computational requirement is lower than that of stochastic and fuzzy LP models. The results of a numeric example further indicated the feasibility and effectiveness of EILP model. In addition, EI nonlinear programming models, hybrid stochastic or fuzzy EILP models as well as risk-based trade-off analysis for EI uncertainty within decision process can be further developed to improve its applicability.     

基于Pythagorean模糊熵的风险型决策方法——考虑后悔与失望规避

针对决策信息为Pythagorean模糊数,属性权重完全未知的风险型多属性决策问题,提出了一种基于Pythagorean模糊熵的考虑决策者后悔与失望规避心理行为的决策方法。首先,计算备选方案和理想点各属性的效用值,从而获得各备选方案的后悔-欣喜值、失望-愉悦值及感知效用值。其次,构建了一种Pythagorean模糊熵,并给出基于该Pythagorean模糊熵的属性权重确定方法,利用属性权重加权求和获得备选方案综合感知效用值,从而对方案进行排序。最后,通过算例说明方法的可行性和优点,并分析了后悔规避系数δ和失望规避系数τ对决策结果的影响。     

A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations

A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconcave value functions are considered.     

Elimination of randomization in statistical decision theory reconsidered

A result by Dvoretky, Wald, and Wolfowitz, (Ann. Math. Statist.22 (1951), 1–21) on the essential completeness of the class of nonrandomized deicision rules is generalized to a statistical decision model with noncompact decision space. The generalized result is obtained as a direct consequence of an existence result for an allocation problem arising in economics.     

Strong reciprocity and strong consistency in pairwise comparison matrix with fuzzy elements

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an \(n\times n\) pairwise comparison matrix. Here, we deal with pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate pairwise comparison matrices with elements from abelian linearly ordered group (alo-group) over a real interval. The concept of reciprocity and consistency of pairwise comparison matrices with fuzzy elements have been already studied in the literature. Here, we define stronger concepts, namely the strong reciprocity and strong consistency of pairwise comparison matrices with fuzzy intervals as the matrix elements (PCF matrices), derive the necessary and sufficient conditions for strong reciprocity and strong consistency and investigate their properties as well as some consequences to the problem of ranking the alternatives.     

Estimation de l'évolution d'un total en présence d'information auxiliaire : une approche par splines de régression

We build an estimator for the evolution of a finite population total between two periods of time when auxiliary information is available. A superpopulation model is introduced in order to explain the relationship between the study and the auxiliary variables. The regression functions are estimated by regression splines and Horvitz–Thompson technique. Finally, an estimator for the evolution is derived and proved to be asymptotically unbiased and consistent and we compute a design-based variance formula. To cite this article: C. Goga, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Nonstationary value-iteration and adaptive control of discounted semi-Markov processes

We consider in this paper discounted-reward, denumerable state space, semi-Markov decision processes which depend on unknown parameters. The problems we are interested in are: Given that the true parameter value is unknown, (I) give an iterative scheme to determine the total maximal discounted reward, and (II) find an asymptotically discount optimal (adaptive) policy. Our solutions are inspired by the nonstationary value iteration (NVI) scheme of Federgruen and Schweitzer (J. Optim. Theory Appl.34 (1981), 207–241) combined with the ideas of Schäl (Preprint No. 428, Inst. Angew. Math. Univ. Bonn, 1981) concerning the “principle of estimation and control” for the adaptive control of semi-Markov processes.     

Classifying efficient alternatives in SMAA using cross confidence factors

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative; the central weight vectors represent the typical preferences favouring each alternative; and the confidence factors measure whether the criteria data are sufficiently accurate for making an informed decision.In some cases, when the problem involves a large number of efficient alternatives, the analysis may fail to discriminate between them. This situation is revealed by low confidence factors. In this paper we develop cross confidence factors, which are based on computing confidence factors for alternatives using each other’s central weight vectors. The cross confidence factors can be used for classifying efficient alternatives into sets of similar and competing alternatives. These sets are related to the concept of reference sets in Data Envelopment Analysis (DEA), but generalized for stochastic models. Forming these sets is useful when trying to identify one or more most preferred alternatives, or suitable compromise alternatives. The reference sets can also be used for evaluating whether criteria need to be measured more accurately, and at which alternatives the measurements should be focused. This may cause considerable savings in measurement costs. We demonstrate the use of the cross confidence factors and reference sets using a real-life example.     

A Descriptive Approach to Multiple-Criteria Decision Making

Certain concepts from multivariate statistical analysis are applied to problems in multiple-criteria decision making. The aim of this approach is to identify basic relationships and conflicts between the available decision alternatives and between criteria. If these aspects can be clearly identified and conveyed to the responsible decision maker, he may well be in a position to make an intelligent selection of a course of action, without the need for formal utility analysis, computation of Pareto optimal sets, etc. Two appropriate multivariate statistical techniques are introduced to illustrate the approach, and each technique is applied to two sample problems.     

A procedure for selection of a multiobjective technique with application to water and mineral resources

The problem of selecting the appropriate multiobjective solution technique to solve an arbitrary multiobjective decision problem is considered. Various classification schemes of available techniques are discussed, leading to the development of a set of 28 model choice criteria and an algorithm for model choice. This algorithm divides the criteria into four groups, only one of which must be reevaluated for each decision problem encountered. The model choice problem is itself modeled as a multiobjective decision problem—strongly influenced, however, by the individual performing the analysis. The appropriate technique is selected for implementation by use of the compromise programming technique. Two example problems are presented to demonstrate the use of this algorithm. The first is concerned with ranking a predefined set of river basin planning alternatives with multiple noncommensurate ordinally ranked consequences. The second deals with coal blending and is modeled by dual objective linear programming. An appropriate multiobjective solution technique is selected for each of these two examples.     

Decision risk analysis for an interval TOPSIS method

TOPSIS is a multi-attribute decision making (MADM) technique for ranking and selection of a number of externally determined alternatives through distance measures. When the collected data for each criterion is interval and the risk attitude for a decision maker is unknown, we present a new TOPSIS method for normalizing the collected data and ranking the alternatives. The results show that the decision maker with different risk attitude ranks the different alternatives.     

A factorization method for elliptic problems in a circular domain

We present a method to factorize a second order elliptic boundary value problem in a circular domain, in a system of uncoupled first order initial value problems. We use a space invariant embedding technique along the radius of the circle, in a decreasing way. This technique is inspired in the temporal invariant embedding used by J.-L. Lions for the control of parabolic systems. The singularity at the origin for the initial value problems is studied. A formal calculation for more general star-shaped domains is presented. To cite this article: J. Henry et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Modeling factions for “effects based operations”: part I—leaders and followers

This paper presents a synthetic approach for generating role playing simulation games intended to support analysts (and trainees) interested in testing alternative competing courses of action (operations) and discovering what effects they are likely to precipitate in potential ethno-political conflict situations. Simulated leaders and followers capable of playing these games are implemented in a cognitive modeling framework, called PMFserv, which covers value systems, personality and cultural factors, emotions, relationships, perception, stress/coping style and decision making. Of direct interest, as Sect. 1.1 explains, is mathematical representation and synthesis of best-of-breed behavioral science models within this framework to reduce dimensionality and to improve the realism and internal validity of the agent implementations. Sections 2 and 3 present this for leader profiling instruments and group membership decision-making, respectively. Section 4 serves as an existence proof that the framework has generated several training and analysis tools, and Sect. 5 concludes with lessons learned. Part II turns to the question of assessment of the synthesis and its usage in course of action studies.

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.     

Reconsideration of the present value method

In investment decision-making, the net present value method is widely used as one of the best decision rules (techniques or criteria). At the same time, it is also used to evaluate decision alternatives for a long range period of time, in economics or even in control theory. Its theoretical validation as the best method for investment decision-making has been based on a basis such that the best technique (investment decision rule) will maximize shareholders' wealth which is measured by the present value of cash flows discounted at the opportunity cost of capital. Such a theoretical requirement as maximizing shareholders' wealth is very important for investment decision-makings. This requirement implies that an ordering relation of projects determined by the best investment rule must be order-isomorphic to that determined by the measure of shareholders' wealth. This order-isomorphism can be represented by necessary and sufficient conditions (or separate criteria). However, they are not suitable for comparing investment decision rules, because they are designed for selecting the best investment decision rule. At the same time, the other dominance of the net present value method over other investment rules is also found in its decision-theoretical aspects. Formulating the net present value method, internal rate of return method and simple sum method in an axiomatic fashion, the net present value method is compared with the other rules, and is shown to have enough clarity and simplicity in theory and practice.