An integrated algebraic approach to conflict resolution with three-level preference

An integrated algebraic approach is developed to calculate stabilities in multiple decision maker graph models with three levels of preference. The algebraic approach establishes an integrated paradigm for stability analysis and status quo analysis under different preference structures, such as two-level preference and three-level preference. Difficulties in coding algorithms to analyze stabilities, rooted in their logical representation, led to the development of matrix representations of preference and explicit matrix calculations to determine stabilities. Here, the algebraic approach is used to represent graph models with three levels of preference and to conduct stability analysis for such models. The algebraic approach facilitates the development of new stability concepts and algorithms to calculate them, and reveals an inherent link between status quo analysis and traditional stability analysis. Hence, it will facilitate the design of an integrated decision support system for the graph model for conflict resolution.     

An interactive procedure for linguistic multiple attribute decision making with incomplete weight information

In this paper, we consider the multiple attribute decision making (MADM) problems, in which the information about attribute weights is partly known and the attribute values are expressed in linguistic labels. We first define the concepts of linguistic positive ideal point, linguistic negative ideal point, and satisfactory degree of alternative. Based on these concepts, we then establish some linear programming models, through which the decision maker interacts with the analyst. Furthermore, we establish a practical interactive procedure for solving the MADM problems considered in this paper. The interactive process can be realized by giving and revising the satisfactory degrees of alternatives till an optimum satisfactory solution is achieved. Finally, a practical example is given to illustrate the developed procedure.     

A BSDE approach to stochastic differential games with incomplete information

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the informed player has to reveal in order to play optimally: to do so, we show that the value function of this zero-sum game can be rewritten as a minimization problem over some martingale measures with a payoff given by the solution of a backward stochastic differential equation.     

An approach to group choice with fuzzy preference relations

This paper presents an approach to group choice with fuzzy preference relations. The experts' judgements are presented as fuzzy preorder relations. As group choice we assume the nearest relation to these relations, in the sense of the Hamming distance. In this paper an algorithm for finding a preorder relation as an expression of group choice is given and a way is pointed out to find the best alternative on the basis of this group choice. Furthermore, the connection between the impossibility theorem of Arrow and this group choice is considered.     

A learning approach to the two person decentralized team problem with incomplete information

A learning approach to the two person decentralized team problem with incomplete information and with a 2X2 payoff matrix is considered. It is shown that if the payoff matrix is unimodal, there exists a proper choice of parameters of the learning algorithm that will ensure asymptotically an expected payoff as close to maximum payoff as desired. It is shown that a team problem with multimodal payoff matrix gives rise to interesting class of open problems.     

残缺语言判断矩阵的可能值推断及决策方法

研究了残缺语言判断矩阵的残缺元素取值范围推断方法及基于残缺语言判断矩阵的决策方法。将残缺语言判断矩阵转化为数值判断矩阵,给出矩阵的满意一致性定义;若矩阵不符合满意一致性,则对矩阵中的已知元素做出适当的修正使其符合一致性要求;同时在允许的偏差范围内求解各方案的权重,并利用可能度方法得到最后的方案排序。     

An interactive dynamic programming approach to multicriteria discrete programming

Several interactive schemes for solving multicriteria discrete programming problems are developed under a dynamic programming framework. It is assumed that the decision maker's preference structure satisfies the conditions of transitivity, monotonicity, and nonsatiation. Hybrid procedures are also structured by including branch and bound ideas into the recursions. Initial computational results are offered.     

An optimal stopping problem with two levels of incomplete information

The following variant of a classical selection problem is considered. Offers of random size are successively available to a decision-maker at discrete time instants, and he has to select one without having the possibility of recall. At any time he can accept or reject the current offer based on some initial information (just received) on its still unknown size, or he can demand additional information and take his decision thereafter. The costc ₀ > 0 for continuing to the next offer and the costd ₀ > 0 for obtaining the additional information are assumed to be constant. Under reasonable conditions on the underlying stochastic structure we find and characterize strategies maximizing the expected net reward.This research was supported in part by a grant from the MINERVA Foundation.     

Dynamic programming: An interactive approach

An interactive approach to the formulation, modeling, analysis, and solution of discrete deterministic dynamic programming problems is presented. The approach utilizes APL both as the mathematical and the programming language. The interactive capabilities of APL and the simple one-to-one correspondence between the programming and the mathematical language provide an extremely convenient environment for dynamic programming investigations in general and for teaching/learning purposes in particular. The approach is illustrated by a simple model and a numerical example.     

Markov games with incomplete information

We consider zero-sum Markov games with incomplete information. Here, the second player is never informed about the current state of the underlying Markov chain. The existence of a value and of optimal strategies for both players is shown. In particular, we present finite algorithms for computing optimal strategies for the informed and uninformed player. The algorithms are based on linear programming results.     

An empirical likelihood approach to quantile regression with auxiliary information

We consider how to incorporate auxiliary information to improve quantile regression via empirical likelihood. We propose a novel framework and show that our approach yields more efficient estimates compared to those from the conventional quantile regression. The efficiency gain is quantified theoretically and demonstrated empirically via simulation studies.     

Finite approximations to a zero-sum game with incomplete information

In this paper, we investigate a scheme for approximating a two-person zero-sum gameG of incomplete information by means of a natural systemG _mn of its finite subgames. The main question is: For largem andn, is an optimal strategy forG _mn necessarily anε-optimal strategy forG?     

An interactive approach for multiobjective decision making

We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations.     

An interactive approach for vector optimization problems

This paper deals with an interactive approach for vector optimization problems. The best compromise solutions are obtained using one of the methods which depends on the global preference, namely Geoffrion's method. The stability set of the first kind is analyzed and used to reduce the parametric space of the problem. An example is given for the sake of illustration.     

An interactive approach for Bi-attribute multi-item auctions

The advances in the technological infrastructure and in the Internet led electronic auctions to become popular. With online sites, people buy/sell inexpensive products/services through auctions. In this paper, we develop an interactive approach that provides aid to both the buyer and the bidders in a bi-attribute, multi-item auction environment. Our approach is applicable for both reverse and forward auctions. We test our approach for underlying linear preference functions of the buyer. We also adapt it as a heuristic for the case the buyer has a nonlinear preference function. The test results show that our approach works well.     

Smoothing preference kinks with information

We identify conditions under which receipt of information in the form of a (potentially) ambiguous signal leads to a smoother maximin expected utility (MEU) preference structure which translates behaviorally into a smaller no-trade price zone. Narrowing of the no-trade price zone depends critically on the rectangularity of the belief structure, which, in the context of an MEU model, is a requirement of dynamic consistency in Machina’s sense. Another important factor affecting the size of the no-trade price zone is the relative contribution of ambiguity in signals and ambiguity in posterior beliefs to the degree of prior ambiguity over market events.     

Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information

A linguistic decision aiding technique for multi-criteria decision is presented. We define a relation between alternatives as multi-criteria semantic dominance (MCSD). It adopts the similar ideal of the stochastic dominance by utilizing the partial information of the decision maker’s preference, which is only ordinal or partially cardinal. The MCSD rules based on three typical types of semanteme functions are introduced and proven. By using these rules, all the alternatives under consideration are divided into two mutually exclusive sets called efficient set and inefficient set. The decision maker who has such a semanteme function will never choose the alternative from the corresponding inefficient set as the optimal one. In such a way, when we analyze the linguistic decision information, the inherent fuzziness of preference can be handled and several controversial operations of the linguistic terms can be avoided. An example is also provided to illustrate the procedure of the proposed method.