Abstract
The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.
Highlights
Multiple attribute decision making (MADM) is a process for selecting the optimal alternative from a set of given alternatives according to some attributes
We developed a picture fuzzy multi-criteria decision making (MCDM) method based on the logarithmic aggregation operators and the logarithmic operations of picture fuzzy set (PFS) to handle picture fuzzy multi-attribute decision making (MADM)
We outlined the logarithmic operational laws of picture fuzzy numbers (PFNs), which are a useful supplement to the existing picture fuzzy aggregation techniques
Summary
Multiple attribute decision making (MADM) is a process for selecting the optimal alternative from a set of given alternatives according to some attributes. IFS is an extension of fuzzy set (FS) [2], which is characterized by a positive membership degree and a negative membership degree, satisfying the condition that the sum of these two degrees is equal to or less than one; IFS is a useful tool in processing fuzzy and uncertainty information. J = βJ a , £J a a ∈ A , is an IFS, where β J a , £ J a ∈ [0, 1] are the positive and negative membership degrees of the element a ∈ A in J, respectively. J = βJ a , γJ a , £J a a ∈ A , is said to be PFS, where β J a , γ J a , £ J a ∈ [0, 1] are the positive, neutral and negative membership degrees of the element a ∈ A in J, respectively.
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