Abstract
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 (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.
Highlights
Multi-attribute decision making and pattern recognition problems are widely used in economy, politics, culture and other fields
We introduce the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator based on the picture fuzzy multiplication operation and the picture fuzzy power operation
Aggregation operator; the PFOWG aggregation operator reduces to IFOWG aggregation operator; PFHG aggregation operator reduces to IFHG aggregation operator
Summary
Multi-attribute decision making and pattern recognition problems are widely used in economy, politics, culture and other fields. Because of the ambiguity and complexity of information, it is very difficult for people to evaluate attributes with real numbers. Fuzzy set theory can be used to deal with fuzzy information effectively, which has attracted the attention of many scholars in fuzzy set theory, and it is applied in many fields. In the process of solving multi-attribute decision and pattern recognition problems, information aggregation is a common activity. Among which, weighted aggregation operators, ordered weighted aggregation operators and hybrid aggregation operators are three common aggregation operators
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