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Open AccessArticle

Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

1
School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
2
School of Software Engineering, Beijing Jiaotong University, Beijing 100044, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 593; https://doi.org/10.3390/sym10110593
Received: 17 October 2018 / Revised: 28 October 2018 / Accepted: 1 November 2018 / Published: 4 November 2018
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed. View Full-Text
Keywords: picture fuzzy set; Dombi t-conorm and t-norm; Heronian mean; picture fuzzy Dombi Heronian mean; multi-attribute decision-making picture fuzzy set; Dombi t-conorm and t-norm; Heronian mean; picture fuzzy Dombi Heronian mean; multi-attribute decision-making
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Zhang, H.; Zhang, R.; Huang, H.; Wang, J. Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making. Symmetry 2018, 10, 593.

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