An axiomatic characterization of different majority concepts

A lot of decision support systems use some kind of aggregation procedure based on the concept of majority, but not always the same one; it can be simple majority, weak majority or one of the many other kinds of majority. This paper attempts to present the main variants of majority and to characterize them in a uniform way. Consequently, it is now easier to compare different kinds of majority and to understand the dissimilarities (or similarities) between them. This should help decision analysts willing to use a majority procedure to choose the right one for their problem and context.     

Handling selection bias when choosing actions in retail credit applications

In many situations one needs to know which action one should take with a customer to yield the greatest response. Typically, estimates of the response functions of different actions will be based on the responses of customers previously assigned to each action. Often, however, the previous assignments will not have been random, so that estimates of the response functions will be biased. We examine the case of two possible actions. We look at the error arising from using the simple OLS estimate ignoring the selection bias, and also explore the possibility of using the Heckman model to allow for the sample selectivity. The performance of Heckman’s model is then compared with the simple OLS through simulation.     

A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations

Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages.     

Decision making in a fuzzy environment and its application to multicriteria power engineering problems

This paper presents results of research into the use of the Bellman–Zadeh approach to decision making in a fuzzy environment for solving multicriteria optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman–Zadeh approach has served as a basis for solving a problem of multicriteria allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision making system (AIDMS1). AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improvment in solution quality. The results of the paper are universally applicable and are already being used to solve power engineering problems. It is illustrated by considering problems of multicriteria power and energy shortage allocation and multicriteria power system operation.     

Sensitivity analysis for product design selection with an implicit value function

In product design selection the decision maker (DM) often does not have enough information about the end users’ needs to state the “preferences” with precision, as is required by many of the existing selection methods. We present, for the case where the DM gives estimates of the preferences, a concept for calculating a “robustness index.” The concept can be used with any iterative selection method that chooses a trial design for each iteration, and uses the DM’s preference parameters at that trial design to eliminate some design options which have lower value than the trial design. Such methods, like our previously published method, are applicable to cases where the DM’s value function is implicit. Our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non-eliminated trial designs (which could be singleton) will not change. The DM, through experience, can use the robustness index and other information generated in calculating the index to determine what action to take: make a final selection from the present set of non-eliminated designs; improve the precision of the preference estimates; or otherwise cope with the imprecision. We present an algorithm for finding the robustness index, and demonstrate and verify the algorithm with an engineering example and a numerical example.     

关于群体决策的偏比映射

本文引进群体决策的决策个体和决策群体关于供选方案对的偏比度,以及偏比泛函概念.由此,定义了群体在供选方案集上的偏比映射,构造了相应的偏比公理系,并且建立了关于群体决策的偏比度分析的基本理论.最后,给出一个利用偏比映射进行群体排序的方法.特别是,文中表明,满足本文所提出的所有偏比公理的偏比映射是存在的.     

群众决策的ακ-较多规则

对于群体决策问题,本文给出一个新的带参数的ακ-较多规则,并且讨论了在此规则下个体选优解和群体选优解的关系。此外,还论证了相应的ακ-较多规则满足Arrow公理的情况。     

Multicriteria modelling for a repair contract problem based on utility and the ELECTRE I method

Each alternative for a repair contract implies a specific responsetime and related cost. The response time is associated withthe commitment of repair time, based on the contract. A decisionmaker chooses the best alternative taking into account the systemperformance and the cost of the contract. This problem has beenanalysed through a multicriteria decision model. This decisionmodel supports decision makers in the determination of the bestcombination of contracting conditions. The decision model proposedallows the decision maker to quantify the consequences of anaction taking into account two basic criteria: the cost of thecontract and the system performance. Two different decisionmodels have been built to support decision makers. These decisionmodels are based on different multicriteria approaches. Thefirst, reported in a previous paper, is based on the multiattributeutility theory (MAUT). The model presented in this paper isbased on the ELECTRE I method combined with utility functions.The paper presents the main theoretical aspects related to bothapproaches and practical implications related to model building.A numerical application is presented in order to illustratethe use of the decision model.     

On the evaluation of strategies for branching bandit processes

Glazebrook [1] has given an account of improved procedures for strategy evaluation for resource allocation in a stochastic environment. These methods are extended in the paper in such a way that they can be applied to problems which, for example, have precedence constraints and/or an arrivals process of new jobs. Theoretical results, backed up by numerical studies, show that quasi-myopic heuristics often perform well.     

Top-Down Fuzzy Decision Making with Partial Preference Information

This paper proposes a multi-stage decision procedure to cope with a hierarchical multiple objective decision environment in which the upper-level DM only provides partial preference information and the lower-level DM is fuzzy about the tradeoff questions such that to achieve substantially more than or equal to some values is delivered to maximize the objectives. Therefore, the procedure consists of two levels, a upper-level and a lower-level. The main idea is that after the upper-level provides partial preference information to the lower-level as a guideline of decision, the lower-level DM determines a satisfactory solution from the reduced non-dominated set in the framework of multi-objective fuzzy programs.