A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric
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ORIGINAL ARTICLE
A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric mean operators Xue Feng1
· Xiaopu Shang1
· Yuan Xu1
· Jun Wang2
Received: 3 January 2020 / Accepted: 2 April 2020 © The Author(s) 2020
Abstract The aim of this paper is to propose a new multi-attribute decision-making (MADM) method to rank all feasible alternatives in complex decision-making scenarios and determine the optimal one. To this end, we first propose the notion of interval-valued q-rung dual hesitant linguistic sets (IVq-RDHLSs) by combining interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) sets with linguistic terms set. The proposed IVq-RDHLSs utilize IVq-RDHF membership and non-membership degrees to assess linguistic terms, so that they can fully express decision-makers’ evaluation information. Additionally, some related concepts such as the operational rules, score and accuracy functions, and ranking method of IVq-RDHLSs are presented. Considering the good performance of the classical Maclaurin symmetric mean (MSM) in integrating fuzzy information, we further generalize MSM into IVq-RDHLSs to propose the interval-valued q-rung dual hesitant linguistic MSM operator, the interval-valued q-rung dual hesitant linguistic dual MSM operator, as well as their weighted forms. Afterwards, we study the applications of IVq-RDHLSs and their aggregation operators in decision-making and propose a new MADM method. Some real decision-making problems in daily life are employed to prove the rightness of the proposed method. We also attempt to demonstrate the advantages and superiorities of our proposed method through comparing with some other methods in this paper. Keywords Multi-attribute decision-making · Interval-valued q-rung dual hesitant fuzzy sets · Interval-valued q-rung dual hesitant linguistic sets · Maclaurin symmetric mean
Introduction The past years have witnessed the great success of the study on Pythagorean fuzzy sets (PFSs) based multi-attribute decision-making (MADM) methods [1–11]. PFSs were proposed by Prof. Yager [12] to overcome the shortcoming of intuitionistic fuzzy sets (IFSs) [13], which they fail to
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Xiaopu Shang [email protected] Xue Feng [email protected] Yuan Xu [email protected] Jun Wang [email protected]
1
School of Economics and Management, Beijing Jiaotong University, Beijing, China
2
School of Economics and Management, Beijing University of Chemical Technology, Beijing, China
describe decision-making situations in which the sum of membership grade (MG) and non-membership grade (NMG) is greater than one. Hence, PFSs have been regarded as an effective tool to comprehensively express decision-makers’ (DMs’) complex evaluation information. Recently, Yager [14] generalized PFSs by relaxing their constraint and proposed the notion of q-rung orthopair fuzzy sets (q-ROFSs). Due to their high efficiency in expressing fuzzy and complex DMs’ assessment information, q-ROFS-based MADM models and methods have been a new research topic in ope
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