Properties of consistent voting systems

We consider exactly and strongly consistent voting functions where the alternative set is the set of real numbers and each person's preference ordering is determined by a utility function ¦x?x^*¦ wherex ^* is his most preferred alternative. We prove that a voting function which is continuous, anonymous, weakly Pareto, and strongly and exactly consistent must coincide with a class of generalized medians studied byMoulin [1978]. Thus, such a function is actually strategyproof. The continuity assumption can be weakened a little, but we give an example of a noncontinuous function which is strongly and exactly consistent, anonymous, and weakly Pareto, but is not strategyproof.     

仓库容量有限条件下的随机存贮管理2

讨论了仓库容量有限条件下的随机存贮管理优化问题,认为时间是连续分布的.对于存贮一种商品的问题,根据订货点和自己仓库容量的关系分两种情况讨论,得到平均损失费与订货点、到货时间之间的关系式,利用实测数据拟合出到货时间的概率密度,建立了以平均损失费用的数学期望为目标函数的最优化模型,并使用MATLAB数学软件进行求解,得到三种商品的最优订货点分别为41,37和36.经过分析得知仓库容量与销售速率的比例、单位商品的损失费均对确定订货点都有重要影响.对于存贮多种商品的问题,根据到货时间的取值范围与两个时间临界点(销售完租借仓库中某种商品的时间和销售完所有该种商品的时间)之间的位置关系,将每种商品分为六种情况,m种商品组合起来,就有6()种不同情况,在此基础上,以m种商品的总体平均损失费用的数学期望作为目标函数,建立问题的最优化模型.针对题目中给出的三种商品的情形进行求解,得到最优订货点L*=4.807.最后,对销售速率随机的情形建立模型并进行了讨论.     

Revisiting the problem of integrability in utility theory

We revisit the problem of integrability in the consumer theory, focusing on the main difficulties. First, we look for a neat and simple local existence result, and then for a global solution. Second, observing that a utility function (or indirect utility function) cannot be determined uniquely, we propose a means to get a kind of uniqueness result. Our approach is coordinate-free and can be used both in the classical case of a finite-dimensional commodity space and in the case an infinite-dimensional model is adopted.     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.     

A Preference Order Dynamic Program for a Knapsack Problem with Stochastic Rewards

In this paper, we extend the knapsack problem to include more realistic situations by treating the rewards (or values) associated with each item included in the solution as random variables with distributions that are known (or may be estimated) rather than known integers, as in the usual formulation. We propose a dynamic programming solution methodology where the usual real-valued return function is replaced by a preference ordering on the distributions of returns from the items selected. In addition to extending previous solutions to the knapsack problem, we demonstrate the selection of a preference ordering criterion and illustrate the conditions required of the ordering to guarantee optimality of the procedure. A sample problem is shown to demonstrate the algorithm, and results of computational experience with 459 problems of varying sizes and parameters are presented.     

超额市场需求函数

本文通过研究超额需求函数与多项式的关系得：（１）对于（ｎ—１）个关于ｐ１,ｐ２…,ｐｎ－１的多项式Ｅ。（ｐ１,ｐ２,…,ｐｎ－１）,ｓ＝１,２,…,ｎ—１,若满足条件：则Ｅｓ,ｓ＝１,２,…,ｎ—１均为一个经济的超额需求函数．（２）对无穷级数ｇ（ｐ）,也存在含有两个消费者与无穷种商品的经济,使得其超额需求函数恰好为ｇ（ｐ）．     

基于效用函数的模糊数的比较与排序

对相同的模糊数进行比较,不同风险偏好的决策者,会得到不同的结论.效用函数是对风险偏好的度量,因此,模糊数的比较与排序的方法,一定要结合决策者的效用函数来构造.为此,根据效用函数定义了模糊效用函数,在此基础上定义了效用序.之后,证明效用序为全序,进一步利用结构元理论对效用序进行表述.根据效用函数反映风险偏好的程度,对效用序进行分类.这样,决策者对模糊数进行比较时,依据自身对风险偏好程度来选择效用序.     

An existence result of a quasi-variational inequality associated to an equilibrium problem

In this paper we consider a Walrasian pure exchange economy with utility function which is a particular case of a general economic equilibrium problem, without production. We assume that each agent is endowed with at least of a commodity, his preferences are expressed by an utility function and it prevails a competitive behaviour: each agent regards the prices payed and received as independent of his own choices. The Walrasian equilibrium can be characterized as a solution to a quasi-variational inequality. By using this variational approach, our goal is to prove an existence result of equilibrium solutions.     

Sensitivity analysis incorporating fuzzy evaluation for scaling constants of multiattribute utility functions

A multiattribute utility function can be represented by a function of single-attribute utility functions if the decision maker’s preference satisfies additive independence or mutually utility independence. Additive independence is a preference condition stronger than mutually utility independence, and the multiattribute utility function is in the additive form if the former condition is satisfied, otherwise it is in the multiplicative form. In this paper, we propose a method for sensitivity analysis of multiattribute utility functions in multiplicative form, taking into account the imprecision of the decision maker’s judgment in the procedures for determining scaling constants (attribute weights).     

群决策中语言信息与其他4种偏好信息的一致化方法

研究语言信息与其他4种偏好信息(偏好次序,效用值,互反判断矩阵,互补判断矩阵)之间的相互转换问题.首先,根据各种偏好信息的实际意义,给出语言信息与他们之间的转换公式,并从理论上证明转换公式的合理性;其次,证明了若语言判断矩阵具有完全一致性,转换后的互反判断矩阵和互补判断矩阵也具有完全一致性;最后用实例验证了转换公式的有效性.     

Utility Representations of Preferences on General Choice Spaces

The purpose of this paper is to reconsider the utility representation problem of preferences. Several representation theorems are obtained on general choice spaces. Preferences having continuous utility functions are characterized by their continuities and countable satiation. It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a continuous utility function is that the preference is continuous and countably satiable. For monotone preferences,we obtain that any space has continuous utility representations.     

Functional ANOVA,ultramodularity and monotonicity: Applications in multiattribute utility theory

Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker’s preference structure. These properties are usually characterized via partial derivatives. However, elicitation methods do not necessarily lead to twice-differentiable utility functions. Furthermore, while in a single-attribute context concavity fully reflects risk aversion, in multiattribute problems such correspondence is not one-to-one. We show that Tsetlin and Winkler’s multivariate risk attitudes imply ultramodularity of the utility function. We demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA). The necessary and sufficient conditions under which monotonicity and/or ultramodularity of single-attribute functions imply the monotonicity and/or ultramodularity of the corresponding multiattribute function under additive, preferential and mutual utility independence are then established without reliance on the utility function differentiability. We also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision-maker’s multivariate risk attitudes.     

Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules

Utility or value functions play an important role of preference models in multiple-criteria decision making. We investigate the relationships between these models and the decision-rule preference model obtained from the Dominance-based Rough Set Approach. The relationships are established by means of special “cancellation properties” used in conjoint measurement as axioms for representation of aggregation procedures. We are considering a general utility function and three of its important special cases: associative operator, Sugeno integral and ordered weighted maximum. For each of these aggregation functions we give a representation theorem establishing equivalence between a very weak cancellation property, the specific utility function and a set of rough-set decision rules. Each result is illustrated by a simple example of multiple-criteria decision making. The results show that the decision rule model we propose has clear advantages over a general utility function and its particular cases.     

区间二型模糊集效用函数和熵在风险决策中的应用

针对以区间二型模糊集(IT2FS)为信息环境的多属性决策(MADM)问题,引入IT2FS效用函数,并提出基于IT2FS效用函数,熵和风险因子的风险决策模型。首先基于截集思想提出两种IT2FS效用函数公式,有效提取了IT2FS全部信息,比以往的序值型公式更加科学有效。其次基于已提出的IT2FS三种不确定度量存在的问题提出三种新型不确定度量,并基于此三种不确定度量提出IT2FS熵公式弥补原有熵度量的不足。再次引入风险偏好因子反映决策者不同的风险态度,并改进风险偏好因子范围。构造基于效用函数,熵和风险偏好因子的风险决策模型。最后利用一个实例分析结果表明,该风险决策模型中决策者风险偏好对属性权重以及方案的排序存在影响,该决策思想对风险投资决策和风险管理决策均有一定的参考作用。     

Representation of preference orderings on Lp -spaces by integral functionals: discounting,continuity and TAS utility

This paper presents an axiomatic approach in a continuous time framework for representing preference orderings on L^p -spaces in terms of integral functionals. We show that if preference orderings on L^p -spaces satisfy continuity, separability, sensitivity, substitutability, additivity and lower boundedness, then there exists a utility function for the preference orderings such that the utility function is an integral functional with an upper semicontinuous integrand satisfying the growth condition. Moreover, if the preference orderings satisfy the continuity with respect to the weak topology of L^p -spaces, then the integrand is a concave integrand. As a result, time additive separable (TAS) utility functions with constant discount rates are obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pointwise Debreu Lexicographic Powers

A linear ordering is Debreu (respectively, pointwise Debreu) if each of its suborderings can be mapped into it with an order-preserving function that is both injective (respectively, locally injective) and continuous (respectively, locally continuous) with respect to the order topology on both spaces. Each Debreu linear ordering is pointwise Debreu, but the converse does not hold. In the context of utility representations in mathematical economics, it has been proved that any lexicographic power with an uncountable exponent fails to be Debreu. We sharpen this result by analyzing lexicographic powers that are pointwise Debreu.     

组合分析法在新产品概念开发与测试中的应用

介绍了组合分析法的基本模型,对2004年海南马自达新上市轿车产品概念测试进行了案例研究,运用组合分析法获得了每个受访者的属性水平效用值、属性相对重要性(偏好权重)、产品总效用函数。在此基础上,根据多属性效用聚类分析的结果获得了轿车配置偏好、价格偏好和变速器偏好三个消费群体。针对这三个属性偏好群体,详细研究了群体属性水平效用、属性相对重要性、产品总效用,模拟了市场占有率及其变化,获得了一些非常有价值的结论。     

公平关切下需求依赖于价格的供应链运作策略研究

在传统的供应链研究中引入零售商公平关切态度,以核心供应商的利润作为公平关切参考点建立零售商的期望效用函数模型,研究三种市场需求模式下零售商公平关切行为倾向对供应链运作的影响。研究结果表明:公平关切零售商的最优定价随公平关切因子和批发价的增加而增大,最优订货随公平关切因子和批发价的增加而减少;传统的批发价契约不能对供应链进行协调,满足一定条件下回购契约可以对公平关切的供应链进行协调;最后,通过数值例子对理论结果进行验证。得到的研究结论可为现实物流企业提供一定的理论参考。     

Pointwise Efficiency in Multiobjective Stochastic Linear Programming

In most of the approaches to the Multiobjective Stochastic Linear Programming problem that have been proposed in the literature, the notion of quality of a solution is not adequately defined. We reconsider this problem from a decision point of view, in contexts where either the decision maker's preference structure cannot be described by a utility function, or where this structure is expressed by an unknown non-decreasing utility function and the probability distribution of the random parameters is unknown. We define a fundamental set of ‘pointwise admissible’ solutions, as well as several subsets of particular interest. We discuss the relevance of these various pointwise efficient sets, their interrelations, and their practical identification.     

考虑专家偏好的创新型企业创新能力评价方法

为解决创新型企业创新能力评价过程中专家偏好差异和指标量纲不一致等问题,文章构建了一个科学的评价指标体系,运用考虑专家偏好的效用函数对创新能力评价指标进行效用估算,并计算灰色关联系数;最后运用TOPSIS方法对创新型企业的创新能力进行综合评价和排序。数值实例证明了该方法的科学性和实用性。