Vladimer Zhukovin, Zurab Alimbarashvili
It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making theory. It will be useful for practice and interesting for scientific research.
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It is introduced the using of generation lexicographical procedure for multicriteria decision-making problems.
In the item there are presented Interval Structure allow to extend the class of multicriteria decision making problems including incomplete Initial Information. this step will facilitate dada gathering in pairs matching for decision making.
We propose a (seemingly) new computationally tractable model for multi-stage decision making under stochastic uncertainty.
We define decision-making functions which arise from studying the multidimensional generalization of the weighted Bajraktarević means. It allows a nonlinear approach to optimization problems. These functions admit several interesting (from the point of view of decision-making) properties, for example, delegativity (which states that each subgroup of decision-makers can aggregate their decisions and efforts), casuativity (each decision affects the final outcome except two trivial cases) and convexity-type properties. Beyond establishing the most important properties of such means, we solve thei…
From this set of procedures for given clause we shall choose only interrogation of experts on pairs decisions. It is widely widespread method. It makes the whole chapter in the theory of the decision-making, well investigated with the formal point of view. In the modern theory of decision-making at gathering the initial information for mathematical model it practically does not have alternative.
When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multi-agent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological mode…
There is given the program realization system "lexicon" by the using lexicographical procedure.
The collective decision-making exhibited by animal groups provides enormous inspiration for multi-agent control system design as it embodies several features that are desirable in engineered networks, including robustness and adaptability, low computational effort, and an intrinsically decentralized architecture. However, many of the mechanistic models for collective decision-making are described at the population-level abstraction and are challenging to implement in an engineered system. We develop simple and easy-to-implement models of opinion dynamics that realize the empirically observed c…
The weighted OWA (WOWA) is a function that aggregates a set of values with weights assigned based on the rank and relative importance of each value. The weighted OWA of uncertain objective functions can generalize many of the criteria that is used in decision making under uncertainty. In this paper, we apply the WOWA criterion to two-stage decision making problems, and present decomposition algorithms to solve them. The algorithms are applied to location-transportation problem with uncertain demands and computational results are presented.
We consider the optimal duration allocation in a decision making queue. Decision making tasks arrive at a given rate to a human operator. The correctness of the decision made by human evolves as a sigmoidal function of the duration allocated to the task. Each task in the queue loses its value continuously. We elucidate on this trade-off and determine optimal policies for the human operator. We show the optimal policy requires the human to drop some tasks. We present a receding horizon optimization strategy, and compare it with the greedy policy.
Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on problems involving multiple stakeholders and a central decision maker. Repetition of the decision-making provides additional opportunities to promote fairness while increasing the complexity from symmetry to finding solutions. This paper presents a general mathematical programming framework for the proposed fairness-over-time (FOT) decision-making problem. The …
According to Blackwell's Theorem it is equivalent to compare channels by either a garbling order or optimal decision making. This equivalence does not hold anymore if also allowing pre-garbling, i. e. for the so-called Shannon-order (see Rauh et al., 2017). We show that the equivalence Fails in general even if the set of decision makers is reduced. This is overcome by the introduction of convexified Shannon-usefulness as a preference relation of decision makers over channels. We prove that convexified Shannon-order and convexified Shannon-usefulness are equivalent.
We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide a…
Decision-Making in Digital Twins: Optimization, Control, and Learning
本文综述数字孪生驱动的决策方法进展，聚焦仿真优化、序列决策、风险感知决策三领域，探讨相关技术并指出研究挑战与机遇。
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an information-theoretic formalization of bounded rational decision-making where decision-makers trade off expected utility and information processing costs. Such bounded rational decision-makers can be thought of as thermodynamic machines that undergo physical state changes when they compute. Their behavior is governed by a free energy functional that trades off changes in internal energy-as a proxy for utility-and entropic changes re…
With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum likelihood parameter estimation problem for softmax decision-making models with linear objective functions. We present conditions under which the likelihood function is convex. These allow us to provide sufficient conditions for convergence of the resulting maximum likelihood estimator and to construct its asymptotic distribu…
Discrete Route/Trajectory Decision Making Problems
本文研究了复合多阶段决策问题，旨在设计从初始决策状态到目标决策状态的路径或轨迹。通过汽车路线问题作为基本物理隐喻，探讨了离散操作/状态设计空间（如有向图）中的多种决策问题，并在教育、医学和经济等领域应用。
Collective Decision-Making in Ideal Networks: The Speed-Accuracy Tradeoff
本文研究人类群体在具有网络交互的模型中进行两种选择任务的集体决策，探讨个体在速度与准确性之间的权衡，通过耦合漂移扩散模型分析证据聚合过程，并探讨网络位置对决策性能的影响。
Double Fuzzy Probabilistic Interval Linguistic Term Set and a Dynamic Fuzzy Decision Making Model based on Markov Process with tts Application in Multiple Criteria Group Decision Making
针对概率语言术语缺陷及动态属性权重确定难问题，提出双模糊概率区间语言术语集概念，定义相关内容，开发模糊语言马尔可夫矩阵等，给出权重确定方法，并用金融风险投资案例说明其在多准则决策中的应用。
On Risk-Sensitive Decision Making Under Uncertainty
本文提出在不确定性下风险敏感决策的最优性条件，并通过最佳投注和库存管理示例验证了理论。
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