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Symmetry 2019, 11(1), 6; https://doi.org/10.3390/sym11010006

Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

School of Business, Sichuan Normal University, Chengdu 610101, China
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Received: 4 December 2018 / Revised: 16 December 2018 / Accepted: 17 December 2018 / Published: 21 December 2018
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
Full-Text   |   PDF [319 KB, uploaded 26 December 2018]

Abstract

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit. View Full-Text
Keywords: MADM; picture fuzzy set (PFS); PFMM operator; PFWMM operator; PFDMM operator; PFWDMM operator; financial investment risk MADM; picture fuzzy set (PFS); PFMM operator; PFWMM operator; PFDMM operator; PFWDMM operator; financial investment risk
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, R.; Wang, J.; Gao, H.; Wei, G. Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk. Symmetry 2019, 11, 6.

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