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Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

机译：决策中的犹豫概率模糊偏好关系

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摘要

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.
机译：相对于另一种替代方案，另一种替代方案是表达决策者观点的有用方法。在小组决策的过程中，在给定标准下，偏好关系用于备选方案的偏好建模。概率是处理不确定性的重要工具。在许多情况下，不同事件的决策概率直接影响决策过程。为了解决这个问题，本文定义了犹豫的概率模糊偏好关系（HPFPR）。此外，在犹豫的概率模糊环境中研究了HPFPR的一致性和决策者之间的共识。在这方面，开发了许多新颖的算法来实现HPFPR的一致性，并在决策者之间达成合理的共识，并提出了一种包含所有其他算法的最终算法，从而为群体决策提供了完整的决策支持模型。最后，我们提供了一个案例研究，对所提出的模型进行了完整说明，并讨论了概率对决策的影响，从而验证了在犹豫的模糊偏好关系中引入概率的重要性。

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