Dimensionality reduction technique under picture fuzzy environment and its application in decision making

The notion of soft matrix plays a vital role in many engineering applications and socio-economic and financial problems. A picture fuzzy set has been used to handle uncertainty data in modeling human opinion. In this work, we recall the picture fuzzy soft matrix concept and its different subsequent classes. Also, different kinds of binary operations over the proposed matrices have been provided. The main contribution of this paper is that using the concept of choice matrix and its weighted form and the score matrix, a new algorithm for decision-making has been outlined by considering the picture of fuzzy soft matrices. The current challenge In the decision-making problems is that many qualitative and quantitative criteria are involved. Hence, the dimensionality reduction technique plays an essential role in simplicity and broader applicability in the decision-making processes. We present an algorithm for the reduction process using the proposed definitions of the object and parameter-oriented picture fuzzy soft matrix and the technique to find the threshold value for the provided information. Then, illustrative numerical examples have also been provided for each proposed algorithm. A detailed comparative study of the proposed techniques has also been carried out in contrast with other existing techniques.