群体多指标决策的偏好集结方法

研究多个指标条件下,利用个体决策结果形成群体一致偏好的方法、假设个体有加性效用函数,将个体多指标效用函数表示成单个指标评价函数的加权和,群体指标评价函数表示成个体指标评价函数的加权和.通过协商指标权重、指标评价函数、支付意愿三个参数,成对个体达成双方一致.提出了(n-1)对个体之间达成双方一致,从而得出群体效用函数的决策方法,这种分析框架同样可以扩展到联盟协商一致中.     

Exploring college students’ mental representations of inferential statistics

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students’ representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students’ partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.     

Avoiding non-optimal management decisions by applying a three-person inspection game

An inspection game models a conflict situation between an inspector and an inspectee. The mathematical analysis aims to generate optimal behavior of the inspectee under the assumption that an undesirable action of the inspectee could otherwise be carried out strategically. In this paper the controller’s (inspector’s) particular job is to audit a manager’s (inspectee’s) decision and to submit a report to the company’s top managers for examination. Thus, a conflict as regards the choice of behavioral actions of the manager, the controller and the top management impends. Based on Fandel and Trockel (2011a) this modified inspection game is discussed here for the first time as a three-person game in the context of a manager’s faulty decision that will unnecessarily add to the company’s costs and that the top management understandably wishes to minimize. We will first examine the conditions under which a Nash equilibrium occurs in this three-person game in which poor management, poor monitoring and poor revision coincide. We will then examine the effects that the penalties and bonuses exert on the Nash equilibrium solution. We will find that penalties and bonuses can neutralize each other in their effects on the improved decision making by the manager and the controller.     

Learning in Dynamic Decision Making: The Recognition Process

The apparent difficulty that humans experience when asked to manage dynamic complexity might be related to their inability to discriminate among familiar classes of objects (i.e., flawed recognition). In this study we examined the change in individuals' recognition ability, as measured by the change in the similarity of decisions they made when confronted repeatedly with consistent dynamic situations of varying degrees of similarity. The study generated two primary findings. First, decisions became increasingly similar with task practice, a result that suggests gradually improving discrimination by the participants. Second, the similarity was determined by the interaction of many task features rather than individual task features. The general principles highlighted by this study are applicable to dynamic situations. For example, with practice, decision makers should be able to learn to identify the time at which to intervene to achieve the maximal effect during dynamic decision making.     

Structuring resource allocation decisions: A framework for building multi-criteria portfolio models with area-grouped options

Multi-criteria portfolio modelling has been extensively employed as an effective means to allocate scarce resources for investment in projects when considering costs, benefits and risks. Some of these modelling approaches allow the grouping of projects into organisational areas, thus also supporting the decision of resource allocation among organisational units in a way that is collectively efficient for the organisation. However, structuring in practice a portfolio model using this latter type of approach is not a trivial task. How should areas be defined? Where should new projects be included? How should one define the criteria to evaluate performance? As far as we know, there is very little indication in the operational research and decision sciences literatures on how to structure this type of model. This paper suggests different ways to structuring portfolio models where projects are divided into areas and evaluated by multiple criteria, and illustrates their use in two action-research projects. Drawing on these experiences it then suggests a general framework for the structuring of such models in practice. Directions for future research are also identified.     

Complete reducibility of gyrogroup representations

Abstract

In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary and hence is completely reducible using strong connections between linear actions of groups and gyrogroups. Also, we provide an example of a unitary representation of an arbitrary finite gyrogroup, which resembles the group-theoretic left regular representation.     

Pointed representations of Virasoro algebra

In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations. This work was supported by CNSF     

Dyadic representations of graphs

A graph $G$ is dyadic provided it has a representation $v\to S_v$ from vertices $v$ of $G$ to subtrees $S_v$ of a host tree $T$ with maximum degree 3 such that $\left(i\right)$$v$ and $w$ are adjacent in $G$ if and only if $S_v$ and $S_w$ share at least three nodes and $\left(ii\right)$ each edge of $T$ is used by exactly two representing subtrees. We show that a connected graph is dyadic if and only if it can be constructed from edges and cycles by gluing vertices to vertices and edges to edges.     

Cross characteristic representations of even characteristic symplectic groups

We classify the small irreducible representations of with even in odd characteristic. This improves even the known results for complex representations. The smallest representation for this group is much larger than in the case when is odd. This makes the problem much more difficult.

     

Construction of tame supercuspidal representations

We give a quite general construction of irreducible supercuspidal representations and supercuspidal types (in the sense of Bushnell and Kutzko) of -adic groups. In the tame case, the construction should include all known constructions, and it is expected that this gives all supercuspidal representations. We also give a conjectural Hecke algebra isomorphism, which can be used to analyze arbitrary irreducible admissible representations, following the ideas of Howe and Moy.

     

Modeling subjective evaluation for fuzzy group multicriteria decision making

This paper presents a new fuzzy multicriteria decision making (MCDM) approach for evaluating decision alternatives involving subjective judgements made by a group of decision makers. A pairwise comparison process is used to help individual decision makers make comparative judgements, and a linguistic rating method is used for making absolute judgements. A hierarchical weighting method is developed to assess the weights of a large number of evaluation criteria by pairwise comparisons. To reflect the inherent imprecision of subjective judgements, individual assessments are aggregated as a group assessment using triangular fuzzy numbers. To obtain a cardinal preference value for each decision alternative, a new fuzzy MCDM algorithm is developed by extending the concept of the degree of optimality to incorporate criteria weights in the distance measurement. An empirical study of aircraft selection is presented to illustrate the effectiveness of the approach.     

Bell representations of finitely connected planar domains

In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate -connected planar domain , where 1$">is representable as with a suitable rational function of degree . This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.

     

The participation puzzle with reference-dependent expected utility preferences

Expected utility theory with a smooth utility function predicts that, when allocating wealth between a risky and a riskless asset, investors allocate a positive amount to the risky asset whenever its expected return exceeds the riskless rate of return. A large number of people invest none of their wealth in risky assets, though, leading to the ”participation puzzle.” This paper explores whether the participation puzzle can be addressed when the utility function has a kink at the reference wealth level. It shows that when the reference wealth level is initial wealth increased by the riskless rate of return, there exists a range of expected excess returns for the risky asset for which the investor takes no position. Moreover, this range of expected excess returns is described by comparing a common performance measure of stock returns, the Omega Function, to a function of preference parameters. However, if the reference wealth level is any other constant, the usual expected utility prediction holds and investors allocate at least some of their wealth to the risky asset whenever it has a positive expected excess return.     

Note on prime representations of convex polyhedral sets

Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant Nos. A8807, A4625, and A7742.     

Binary terms in polynomial representations of Boolean functions

Polynomial representations of Boolean functions by binary terms are considered. The construction of terms involves variables and residual functions. Special cases of such representations are the decomposition of a function with respect to variables, Zhegalkin polynomials, and representations of functions as sums of conjunctions of residual functions.     

Construction of rigid local systems and integral representations of their sections

We give a method for constructing all rigid local systems of semi‐simple type, which is different from the Katz–Dettweiler–Reiter algorithm. Our method follows from the construction of Fuchsian systems of differential equations with monodromy representations corresponding to such local systems, which give an explicit solution of the Riemann–Hilbert problem. Moreover, we show that every section of such local systems has an integral representation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)