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Open AccessArticle

Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
2
School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(7), 608; https://doi.org/10.3390/math7070608
Received: 17 May 2019 / Revised: 27 June 2019 / Accepted: 1 July 2019 / Published: 8 July 2019
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. View Full-Text
Keywords: logarithmic operational laws; logarithmic picture fuzzy aggregation operators; decision making problems logarithmic operational laws; logarithmic picture fuzzy aggregation operators; decision making problems
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MDPI and ACS Style

Khan, S.; Abdullah, S.; Abdullah, L.; Ashraf, S. Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems. Mathematics 2019, 7, 608. https://doi.org/10.3390/math7070608

AMA Style

Khan S, Abdullah S, Abdullah L, Ashraf S. Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems. Mathematics. 2019; 7(7):608. https://doi.org/10.3390/math7070608

Chicago/Turabian Style

Khan, Saifullah; Abdullah, Saleem; Abdullah, Lazim; Ashraf, Shahzaib. 2019. "Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems" Mathematics 7, no. 7: 608. https://doi.org/10.3390/math7070608

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