Bi-Topological Pythagorean Fuzzy Soft Set in R-Programming

In modern business scenarios, decision making involves multiple parameters such as product rating, profit, price which often contain vagueness and imprecision. This study proposes a Bi-Topological Pythagorean Fuzzy Soft Set (BTPFSS) based decision-making framework for product evaluation and demand prediction under uncertain environments. Traditional decision models are not effective in handling such uncertainty. To overcome this limitation, the proposed framework integrates Pythagorean fuzzy sets, soft set theory, and bi-topological structures to represent uncertain information more effectively.

The computational implementation of the proposed model is developed using R programming language and the Shiny framework, which enables the creation of an interactive decision support dashboard. Product data collected from Excel files are converted into Pythagorean fuzzy membership and non-membership values, and these values are used to construct the bi-topological fuzzy soft structure. The system evaluates multiple decision alternative and identifies optimal products using mechanism.

In addition, the framework incorporates decision tree classification techniques to analyze product demand patterns and support market trend prediction. The proposed system assists organizations in selecting profitable products, improving demand forecasting, and enhancing inventory management. The results demonstrate that the integration of fuzzy mathematical models with data-driven analytical tools provides an efficient approach for decision making under uncertain business environments.