Multiple-criteria decision making method based on the scaled prioritized operators with unbalanced linguistic informatio
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Multiple‑criteria decision making method based on the scaled prioritized operators with unbalanced linguistic information Peide Liu1 · Weiqiao Liu2
© Springer Nature B.V. 2020
Abstract The unbalanced linguistic terms set (ULTS) is a special linguistic term set which can describe the vagueness assessment that is non-uniform and non-symmetrical distributed. So, it is effective to describe the uncertainty information existed in some special real decision making problems by ULTS. As a special prioritized operator, the scaled prioritized (SP) operator has the advantage of taking the priority among different criteria into account by detailed priority labels in known case and unknown case. In this paper, we combine the merits of SP operators and ULTS for dealing with some special multi-criteria decision making (MCDM) problems where there is a priority relationship between criteria under ULTS evaluation information. We present the unbalanced 2-tuple linguistic scaled prioritized averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric averaging operator, which can handle the issues of the detailed priority relationship among different categories of MCDM problems in knowable case. Further, we propose the unbalanced 2-tuple linguistic scaled prioritized weighted averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric weighted averaging operator, which can deal with the case when the detailed priority relationship among different categories of different criteria is unknowable. Then, we discussed several characteristics of the proposed operators, such as boundedness, monotonicity, and idempotency. Besides, we presented an approach for the MCDM problems according to the proposed operators. In the last, we provide an example to explain the calculating steps and effectiveness of these methods. Keywords Scaled prioritized operator · Unbalanced linguistic terms set · Multi-criteria decision making
* Peide Liu [email protected]; [email protected] 1
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, People’s Republic of China
2
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu, People’s Republic of China
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P. Liu, W. Liu
1 Introduction Since Churchman et al. (1957) introduced the MCDM approaches, the theory and methods of MCDM in some certain situations have been perfect developed. However, in our real decision problems, the assessment values of criteria are not always shown as a certain value because of the uncertainty and fuzziness. So, in many times, it is more rational to be expressed by fuzzy information (Chen et al. 2013; Xu and Yager 2006; Yu and Wu 2012), such as fuzzy numbers (FNs) (Kang et al. 2019; Li 2005; Liu and Wang 2019), linguistic variables (LVs) (Liu 2018), and so on (Morente-Molinera et al. 2019; Zhang et al. 2019). Compared with fuzzy numbers, the LVs are more suitable to deal with qualita
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