Abstract
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.
Highlights
Decision-making science is an ancient and dynamic discipline
We investigate the influence of parameters p and q on the scores and ranking orders in the Picture Fuzzy Dombi Weighted Geometric Heronian Mean (PFDWGHM) operators
The proposed method based on Picture Fuzzy Dombi Weighted Heronian Mean (PFDWHM) operator (λ = 2, p, q = 1 )
Summary
Decision-making science is an ancient and dynamic discipline. In daily life and the management of companies, we often encounter decision-making problems. If a decision-maker thinks the membership degree is 0.2, the membership degree is 0.3, and the degree that he/she is not sure about the result is 0.1, the decision-maker’s evaluation value can be denoted as (0.2, 0.1, 0.3), which cannot be represented by IFSs. In order to deal with this case, Cuong [35] proposed the concept of picture fuzzy set (PFS), characterized by a positive membership degree, a neutral membership degree, and a negative membership degree. Dombi t-conorm and t-norms have not been applied to the aggregation of PFNs. it is necessary to extend Dombi t-conorm and t-norms to PFNs and propose new operational laws of PFNs. Secondly, all the picture fuzzy aggregation operators do not consider the interrelationship among PFNs. attributes in most real MADM problems are correlated, meaning the interrelationship between attribute values should be considered when aggregating them.
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