A note on Grzegorczyk's logic

Grzegorczyk's modal logic (Grz) corresponds to the class of upwards well‐founded partially ordered Kripke frames, however all known proofs of this fact utilize some form of the Axiom of Choice; G. Boolos asked in [1], whether it is provable in plain ZF. We answer his question negatively: Grz corresponds (in ZF) to a class of frames, which does not provably coincide with upwards well‐founded posets in ZF alone. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Direct Approach to Group Decision Making with Uncertain Additive Linguistic Preference Relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of uncertain additive linguistic preference relations. We define the concept of uncertain additive linguistic preference relation, and introduce a formula based on possibility measure for comparing two uncertain linguistic preference values. We introduce some aggregation operators such as the uncertain linguistic averaging (ULA) operator and uncertain linguistic weighted averaging (ULWA) operator, etc. Based on the ULA and ULWA operators, we develop a direct approach to group decision making with uncertain additive linguistic preference relations without loss of information. Finally, an illustrative numerical example is given to verify the developed approach.     

Nash equilibria for non-binary choice rules

We prove the existence of equilibria in games with players who employ abstract (non-binary) choice rules. This framework goes beyond the standard, transitive model and encompasses games where players have non-transitive preferences (e.g., skew-symmetric bilinear preferences).      

美容院顾客满意度影响因素的实证分析

本文通过对国内外美容行业现状的分析,以长沙市美容院顾客满意度的问卷调查结果为依据,利用统计研究的方法进行分析,得出了几个影响顾客满意度的关键因素,指出美容院行业在产品和销售服务等方面存在多种管理经营缺陷。     

Characterization of rankings generated by linear discriminant analysis

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.     

Indefinite preference structures and decision analysis

It always takes time for people to digest information and make judgments. The decision maker's preference is not always clear and stable when decision analysis and decision making are performed. In this paper, we introduce a generalized preference structure to cope with indefinite preferences. We describe its general properties, its implication on value function representation, its solution concepts, and methods for obtaining the solutions.This research has been partially supported by NSF Grant No. IST-84-18863. The authors are grateful to Dr. D. J. White for his helpful comments on a previous draft.     

Some equivalents of AC in algebra II

We show that the axiom of choice AC is equivalent to the statement Any quotient group of any abelian group has a selector. We also show that the multiple choice axiom MC is equivalent to the assertion: Any filter in any Boolean ring has a well ordered filterbase. Received October 3, 1996; accepted in final form May 1, 1998.     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

夏普里值在顾客满意度测评中的应用研究

利用夏普里值来识别导致顾客不满意的质量属性.因为夏普里值差异很小的质量属性具有高度的相关性,所以可以把具有相同或者类似的夏普里值的质量属性划分为同类属性,从而能够识别导致顾客不满意的质量属性.算例进一步验证该方法的可行性和正确性.