PARETO EQUILIBRIA OF MULTICRITERIA GAMES WITHOUT COMPACTNESS，CONTINUITY AND CONCAVITY

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Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier

New hybrid methods for approximating the Pareto frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto frontiers are considered. Since the approximation of the Pareto frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.     

一个具有两类工件的多目标排序的多项式时间算法

本文考虑具有两个工件集的单机排序问题.第一个工件集J1以完工时间和为目标函数,第二个工件集J2以最大加权完工时间为目标函数.问题的目标是寻找一种排序,使得两个目标函数的加权和达到最小.本文证明该问题可在O(n1n2(n1 n2))时间内求解.     

Implementing stochastic multicriteria acceptability analysis

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision.     

Solution concepts in continuous-kernel multicriteria games

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.This paper is based partially on research supported by the Council of Scientific and Industrial Research, India, through a Research Associateship Grant to the first author.The authors are grateful to two anonymous referees for suggesting useful changes and pointing out some errors in a previous draft.     

基于直觉模糊集的多准则模糊决策问题

提出了一种基于直觉模糊集处理模糊决策问题的新方法.该方法用直觉模糊集描述方案关于准则集的满足程度与不满足程度.而且该方法允许决策者给出准则对于模糊集“重要”的隶属度与非隶属度,即准则的权重也由直觉模糊集表示.这种方法为决策者做出最优决策提供了一种方便有效的方法.     

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.     

Organizational Design of Post Corporation Structure Using Fuzzy Multicriteria Decision Making

A model for organizational design of post corporation structure is developed in this paper. Alternative organization solutions have been designed taking into account the post environment characterized by private operators' competition and development of new message transmission technologies. Criteria for organizational design have been considered as numerical and uncertain linguistic variables describes by fuzzy sets. The model has been tested on a numerical example.     

Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.     

The Advantages of Fuzzy Optimization Models in Practical Use

Classical mathematical programming models require well-defined coefficients and right hand sides. In order to avoid a non satisfying modeling usually a broad information gathering and processing is necessary. In case of real problems some model parameters can be only roughly estimated. While in case of classical models the vague data is replaced by "average data", fuzzy models offer the opportunity to model subjective imaginations of the decision maker as precisely as a decision maker will be able to describe it. Thus the risk of applying a wrong model of the reality and selecting solutions which do not reflect the real problem can be clearly reduced. The modeling of real problems by means of deterministic and stochastic models requires extensive information processing. On the other hand we know that an optimum solution is finally defined only by few restrictions. Especially in case of larger systems we notice afterwards that most of the information is useless. The dilemma of data processing is due to the fact that first we have to calculate the solution in order to define, whether the information must be well-defined or whether vague data may be sufficient. Based on multicriteria programming problems it should be demonstrated that the dilemma of data processing in case of real programming problems can be handled adequately by modeling them as fuzzy system combined with an interactive problem-solving. Describing the real problem by means of a fuzzy system first of all only the available information or such information which can be achieved easily will be considered. Then we try to develop an optimum solution. With reference to the cost-benefit relation further information can be gathered in order to describe the solution more precisely. Furthermore it should be pointed out that some interactive fuzzy solution algorithms, e.g. FULPAL provide the opportunity to solve mixed integer multicriteria programming models as well.