An overview of probabilistic-based expressions for qualitative decision-making: techniques, comparisons and developments
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ORIGINAL ARTICLE
An overview of probabilistic-based expressions for qualitative decision-making: techniques, comparisons and developments Zeshui Xu1,2 · Yue He1 · Xizhao Wang3 Received: 31 January 2018 / Accepted: 23 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract The rapid development of science and technology brings the complexity and difficulty in decision-making. As a comprehensive tool for information expression, the probabilistic-based expressions can denote the complex information by considering the hesitancy and the accuracy at the same time. Because of the flexibility for expression, the related researches of the probabilistic-based expressions develop at a high rate of speed even though they are not systematical and mature enough. In this paper, we introduce the existing concepts of the probabilistic-based expressions and deeply analyze their developments and compare their similarities and differences. Each kind of concept has its own advantages and limitations, and can be applied for different decision-making environments. Besides, we investigate the research status of the techniques of the probabilistic-based expressions since they are the basis for most decision-making methods. For now, the existing decisionmaking methods for probabilistic-based expressions can be divided into the multi-attribute decision-making methods and the dynamic decision-making methods. It is worthy to point out that there are still a lot of severe challenges in the development process of probabilistic-based expressions, but their theoretical and applied value deserves to be paid much attention. Keywords Probabilistic-based expressions · Probabilistic linguistic term sets · Distribution assessment · Probabilistic hesitant fuzzy sets · Ordinal information
1 Introduction Due to the rapid development of modern technology, the communication between the people, the companies and the government is becoming convenient and simple. Thus, at the same time, the environment for decision-making may be uncertain and vague, and the structures of information are also more and more complex. The numerical values cannot * Zeshui Xu [email protected] Yue He [email protected] Xizhao Wang [email protected] 1
Business School, Sichuan University, Chengdu 610064, China
2
School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
3
College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China
express the uncertain information appropriately, and the linguistic term set [1] and the fuzzy set [2] and their extensions [3–7] have already been proven to be effective and suitable to be applied in supply chain [8–11], human resource management [12–15] and hospital management [16–19], etc. But when dealing with the group decision-making problems, each decision maker needs to provide a decision matrix or a preference relation, which is inefficient and wastes the space of data storage during the era of bid data. Thus,
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