A new approach to cubic q-rung orthopair fuzzy multiple attribute group decision-making based on power Muirhead mean
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ORIGINAL ARTICLE
A new approach to cubic q-rung orthopair fuzzy multiple attribute group decision-making based on power Muirhead mean Jun Wang1 • Xiaopu Shang2 • Kaiyuan Bai3 • Yuan Xu2 Received: 20 August 2019 / Accepted: 21 February 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The q-rung orthopair fuzzy sets (q-ROFSs) have been proved to be an efficient tool in expressing decision makers’ (DMs) evaluation values in multiple attribute group decision-making (MAGDM) procedure. To more effectively represent DMs’ evaluation information in complicated MAGDM process, this paper proposes a new tool, called cubic q-rung orthopair fuzzy sets (Cq-ROFSs), based on the combination of q-ROFSs with interval-valued q-ROFSs. Then, we investigate MAGDM problems in which DMs’ preference information is given in terms of cubic q-rung orthopair fuzzy numbers. First, the definition, operations and comparison method of Cq-ROFSs are introduced. Second, to effectively aggregate cubic q-rung orthopair fuzzy information we propose the cubic q-rung orthopair fuzzy power average operator, the cubic q-rung orthopair fuzzy power Muirhead mean operator as well as their weighted forms. We illustrate the powerfulness and flexibility of the proposed operators in fusing cubic q-rung orthopair fuzzy decision-making information. Third, on the basis of the proposed operators we give the main steps of a novel cubic q-rung orthopair fuzzy MAGDM method. We utilize the method to solve real MAGDM problems to prove its effectiveness and validity. Finally, we explain why DMs should choose our proposed method rather than some others through comparison analysis. Keywords Cubic q-rung orthopair fuzzy sets Power average operator Muirhead mean Cubic q-rung orthopair fuzzy power Muirhead mean Multiple attribute group decision-making
1 Introduction As a popular and interesting research topic in the field of modern decision-making sciences, multi-attribute group decision-making (MAGDM) theories and methods have received much attention [1–10]. Due to the high complexity of practical MAGDM problems, it is almost impossible for decision makers (DMs) to obtain all the information of feasible alternatives related to the decisionmaking problems. Hence, there exist fuzziness and uncertainty in actual MAGDM problems and how to effectively & Xiaopu Shang [email protected] 1
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China
2
School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
3
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
handle such kind of vagueness is key to select the optimal alternative. Many scientists and scholars have devoted themselves to discover methodologies that can effectively represent fuzzy decision-making information in MAGDM procedure. The past decades have witnessed the great developments of fuzzy sets theories. In [11],
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