Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

• Main Authors: Minxia Luo, Huifeng Long
• Format: Article
• Language: English
• Published: MDPI AG 2021-01-01
• Series: Symmetry
• Subjects: picture fuzzy sets; aggregation operators; multi-attribute decision making; pattern recognition
• Online Access: https://www.mdpi.com/2073-8994/13/1/119

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (<inline-formula><math display="inline"><semantics><mrow><mi>P</mi><mi>F</mi><mi>W</mi><mi>G</mi></mrow></semantics></math></inline-formula>) aggregation operator, the picture fuzzy ordered weighted geometric (<inline-formula><math display="inline"><semantics><mrow><mi>P</mi><mi>F</mi><mi>O</mi><mi>W</mi><mi>G</mi></mrow></semantics></math></inline-formula>) aggregation operator and the picture fuzzy hybrid geometric (<inline-formula><math display="inline"><semantics><mrow><mi>P</mi><mi>F</mi><mi>H</mi><mi>G</mi></mrow></semantics></math></inline-formula>) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.