A hierarchical game under uncertainty conditions with using player risk function and guarantied strategy estimate

A game-theoretic model of optimal interaction of players in a two-level hierarchic system under uncertainty conditions is proposed. The players keep in mind the outcome with the worst value of the uncertain factor, so that the upper-level player also applies guaranteed approach to the lower-level player. The convergence of the type of penalty function method we use has been proved, the problem of passing from iterated limits by the penalty parameters to the conventional limit by means of their match has been solved. The optimality conditions were obtained.     

Two problems of control under conditions of uncertainty

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 114–121, July–August, 1993.     

Multicriteria optimization of technological processes under uncertainty conditions

The multicriteria optimization problem under uncertainty conditions is considered, which arises at the design stage of a technological process. The uncertainty stems from the inaccuracy of mathematical models and a certain uncertainty of the conditions in which the process will be implemented. The generalization is treated of well known multicriteria optimization methods in the case of the uncertainty accounting. Here, account will be taken of the possibility of the use of control variables at the operation stage to compensate for the uncertainty effect.     

Suboptimal control of logical-dynamic systems under parametric uncertainty conditions

Sufficient optimality conditions of logical-dynamic systems are obtained, the logical portion of which models the operation of a memory-equipped automaton. Equations are derived for the definition of the optimal programmed control and full feedback control. Optimal processes with multiple switchings of the logical (automaton) portion at fixed instants of time are investigated. On the basis of sufficient conditions, algorithms are suggested for the development of the suboptimal control of logical-dynamic systems under parametric uncertainty conditions. The use of optimality and suboptimality conditions is illustrated by examples.     

A cooperative game theory based user-centered medical device design decision approach under uncertainty

The medical device conceptual design decision-making is a process of coordinating pertinent stakeholders, which will significantly affect the quality of follow-up market competitiveness. However, as the most challenging parts of user-centered design, traditional methods are mainly focusing on determining the priorities of the evaluation criteria and forming the comprehensive value (utility) of the conceptual scheme, may not fully deal with the interaction and interdependent between the conflicts of interest among stakeholders and weigh the ambiguous influence on the overall design expectations, which results in the unstable decision-making results. To overcome this drawback, this paper proposes a cooperative game theory based decision model for device conceptual scheme under uncertainty. The proposed approach consists of three parts: first part is to collect and classify needs of end users and professional users based on predefined evaluation criteria; second part is using rough set theory technique to create criteria correlation diagram and scheme value matrix from users; and third part is developing the fuzzy coalition utility model to maximize the overall desirability through the criteria correlation diagram with the conflict of interests of end and professional users considered, and then selecting the optimal scheme. A case study of blood pressure meter is used to illustrate the proposed approach and the result shows that this approach is more robust compared with the widely used the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach.     

On the solution of hierarchical game under uncertainty with total risk of players

In the paper a static two-level hierarchical game under uncertainty conditions is investigated. The guaranteed Nash equilibrium is constructed between players of levels, which is based on the total risk function. It is shown, that the proposed equilibrium for this game is partially interchangeable with another equilibrium situation and cannot be improved. Properties of the risk function are revealed. The algorithm of solving the game is given and an example is considered.     

Coping with uncertainty in a location-based game

With location-based games, how you manage uncertainty can make the difference between fun and fiasco. Game designers should know what uncertainties to hide and what to reveal to create an engaging experience. This article describes our experiences, focusing on uncertainty, in publicly deploying an experimental, mobile mixed-reality game called Can You See Me Now?.     

On the use of computers in planning under conditions of uncertainty

In this paper there are presented some recent results in stochastic linear programming which require for obtaining numerical solutions mainly the existing efficient programs for linear and quadratic programming. It is also shown that for stochastic linear programs with simple randomization the minimum risk solution does not depend on the probability distribution of coefficients and can be obtained by linear programming. The relevance of the results to planning under uncertainty is illustrated and numerical examples and computation experience is reported. All the methods presented can provide numerical results for problems of dimensions met in applications.     

Finite cooperative games with a parametric concept of equilibrium under uncertainty conditions

The parametric concept of equilibrium (the optimality principle) in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of the players into coalitions. In this situation, two extreme cases of this partitioning correspond to the lexicographically optimal situation and the Nash equilibrium situation, respectively. The analysis of the stability of a generalized optimal situation under the perturbations of the coefficients of the linear payoff functions in the l ₁-metric is performed. The limiting level of such perturbations, conserving the optimality of the situation is found.     

On continuous strategies of deviation from a nonconvex set under uncertainty conditions

Studies are made of continuous methods of the deviation in one differential game on the plane with a nonconvex terminal set. The game is nondegenerate in the sense that the programmed controls give no way of affording the deviation and there exists a (discontinuous) method of feedback control that guarantees the deviation. The problem under study can serve as an example of the nondegenerate differential game with a nonconvex terminal set, in which the attempt fails to assure the deviation with the aid of feedback control methods described by continuous mappings. Strategies are investigated that satisfy the Caratheodory conditions and contain the argument deviation. Despite the nonconvexity of the terminal set, by which the circumference serves, it is possible to perform the proof of the unsolvability with the aid of a rather simple mathematical technique on the basis of the Schauder theorem for the fixed point.     

不确定条件下循环供应链模糊自适应生产计划调度

首先,建立了循环供应链下生产计划调度模型和状态方程,通过模糊量化因子整合了正向和逆向生产计划,分析了循环供应链中存在的不确定性.然后,设计一种模糊自适应生产计划调度模型,对循环供应链生产计划的需求信息、回收信息、库存信息和生产信息进行模糊化,通过对生产计划量的自适应比例-积分-微分处理,提高了生产系统的产出对需求信息及回收信息的快速响应.最后,对该模型的应用进行了讨论和仿真验证.     

Regularization of problem of processing measurement data under conditions of a priori uncertainty

Using regularization procedures, the problem of identification of the parameters of nonlinear objects with minimal a priori information on the probabilistic characteristics of the measurement noise and disturbandes is solved on the basis of the conception of the inverse problems of dynamics. The algorithm which is obtained remains stable in the presence of errors in the input data and is oriented towards the contemporary capabilities of computer engineering. Results of a numerical experiment are presented.     

A statistical minimax approach to optimizing linear models under a priori uncertainty conditions

A statistical minimax method for optimizing linear models with parameters, given up to the accuracy of belonging to some uncertainty sets, is proposed. Statistical methods for constructing uncertainty sets as confidence regions with a given reliability level are presented. A numerical method for finding a minimax strategy is proposed for arbitrary uncertainty sets that meet convexity and compactness conditions. A number of examples are considered that admit the analytical solution to optimization problem. Results of numerical simulation are given.     

Multicriteria decision making under conditions of uncertainty in application to multiobjective allocation of resources

This study is concerned with a multiobjective allocation of resources (or their shortages), delivering an answer to the fundamental question “How to do?” arising in different types of planning activities (strategic, innovation, new business, research and development, expansion, operational, maintenance, etc. planning). The solution to the problem is associated with the extension of the general scheme of multicriteria decision making under uncertainty. This scheme is based on a possibilistic approach and involves a fuzzy set-based generalization of the classic approach to deal with the uncertainty to produce solutions, including robust solutions, in multicriteria analysis. Its usage, in the original form, helps one to use available quantitative information to the highest extent to reduce the decision uncertainty regions. If the quantitative information does not lead to a unique solution, the scheme presumes the application of information of qualitative character (based on knowledge, experience, and intuition of experts) used at the final decision stage. However, increasingly, we encounter problems whose essence requires the consideration of the objectives (investment attractiveness, political effect, maintenance flexibility, etc.) formed on the basis of qualitative information, at all decision process stages. Considering this, the study is aimed at generating multicriteria solutions, including multicriteria robust solutions, by constructing representative combinations of initial data, states of nature or scenarios with direct using qualitative information (with the possibility for experts to apply diverse preference formats processed by transformation functions) presented along with quantitative information, realizing a process of information fusion within the multiobjective models. The corresponding results are of a universal character and applicable to diverse classes of multiobjective problems. The paper also proposes a new approach to the homogeneous and expert-acceptable formulation of specific allocation objectives. Examples are presented to illustrate the study results.     

Automatic methods of useful signals extraction from noise background under conditions of nonparametric uncertainty

Three basic techniques for random signals processing are under study: the problems of filtration, interpolation, and prediction. The last advances (including those of the author) in finding smoothing parameter (bandwidth) in the problems of nonparametric kernel estimation of unknown probability densities and their derivatives made it possible to advance further in the theory of the nonparametric estimation of signals with unknown distribution. This progress gave rise to the evolution of automatic methods for signals extraction from noise under the conditions of nonparametric uncertainty. The word “automatic” is understood in the sense that the suggested methods for processing signals depend only on the observable sample. In the article, by the simple example of the additive model, the comparison is made of the nonparametric procedures for the signals processing with the known optimal processing procedures obtained at the complete statistical information about the signals and noise distributions. The results of computer modeling show that the accuracy of nonparametric signals estimates insignificantly gives up to the accuracy of optimal estimates.     

Combinatorial optimization under uncertainty

In this paper, the general problem of Euclidean combinatorial optimization under uncertainty is formulated for the first time and the concepts of a stochastic multiset, a multiset of fuzzy numbers, a stochastic Euclidean combinatorial set, and general Euclidean combinatorial set of fuzzy stochastic numbers that combines the properties of both types of uncertainty are introduced. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 35–44, September–October 2008.