基因组重排问题的一个近似算法

分子生物学中基因无方向的反向基因组重排问题在数学上已被证明是一个NP困难问题．基于断点图的概念，给出一个时间复杂性为O(max{b^(π)，nb(π)})，空间复杂性为0(n)的求其近似最优解的算法．其中n为基因组中基因个数，π=(π1,π2，…，πn)表示n个基因的一种排列，b(π)表示排列π中的断点数．数据实验的结果表明，该近似算法可以求得较好的结果．     

Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Stochastic preference analysis in numerical preference relations

Numerical preference relations (NPRs) consisting of numerical judgments can be considered as a general form of the existing preference relations, such as multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), interval MPRs (IV-MPRs) and interval FPRs (IV-FPRs). On the basis of NPRs, we develop a stochastic preference analysis (SPA) method to aid the decision makers (DMs) in decision making. The numerical judgments in NPRs can also be characterized by different probability distributions in accordance with practice. By exploring the judgment space of NPRs, SPA produces several outcomes including the rank acceptability index, the expected priority vector, the expected rank and the confidence factor. The outcomes are obtained by Monte Carlo simulation with at least 95% confidence degree. Based on the outcomes, the DMs can choose some of them which they find most useful to make reliable decisions.     

Accept & reject statement-based uncertainty models

We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss—as a bridge to existing frameworks—a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.     

Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.     

An integrated operation module for individual risk management

In this study, we used the cumulative prospect theory to propose the individual risk management process (IRM) which includes risk analysis and risk response stages. According to an individual’s preferential structure, the process has been developed into an operational module which includes two sub-modules. From this, the individual’s risk level for the confronted risk can be identified from the risk analysis, while the response strategies can be assessed at the risk response stage. Therefore, optimal response strategies can be recommended based on individual risk tolerance levels.     

Ordered sets with interval representation and (m,n)-Ferrers relation

Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that we call “d-weak orders”, “d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation.     

The representability number of a chain

For each pair of linear orderings (L,M), the representability number repr_M(L) of L in M is the least ordinal α such that L can be order-embedded into the lexicographic power . The case is relevant to utility theory. The main results in this paper are as follows. (i) If κ is a regular cardinal that is not order-embeddable in M, then repr_M(κ)=κ; as a consequence, for each κω₁. (ii) If M is an uncountable linear ordering with the property that A×_lex2 is not order-embeddable in M for each uncountable AM, then for any ordinal α; in particular, . (iii) If L is either an Aronszajn line or a Souslin line, then .     

模糊全半序结构

以Fodor公理为基础，给出一类重要的模糊偏好结构——模糊全半序结构的一个较为一般的定义，同时对其性质进行讨论。