Parametric picture fuzzy cross-entropy measures based on d-Choquet integral for building material recognition

This research paper introduces a novel picture fuzzy cross-entropy measure that utilizes Lin's divergence as a basis for comparing two picture fuzzy sets. To improve the flexibility and applicability of this new cross-entropy measure, a family of parametric cross-entropy measures is defined. By adjusting the parameters in applications, the influence of the degree of positive membership, negative membership, and neutral membership on the picture fuzzy cross-entropy can be observed, allowing for a more tailored analysis. Additionally, we investigate the relationship between power weighted means and the d-Choquet integral, which serves as an extension of the ordinary Choquet integral. Using this knowledge, picture fuzzy cross-entropy measures based on the d- Choquet integral are introduced to yield more sensitive results, particularly when interactions between criteria exist in specific problem domains. This consideration of criterion interactions is often absent in existing cross- entropy measures. Moreover, an algorithm is presented for solving pattern recognition problems and applied to a building material recognition problem sourced from existing literature. Then, we proposed another algorithm and use it to investigate a novel material classification problem. Through these applications, the effectiveness of the proposed cross-entropy measures in pattern recognition is demonstrated. The paper conducts a comparative analysis between existing methods and the proposed approaches, followed by a sensitivity analysis. This analysis involves manipulating the parameters derived from both the parametric cross-entropy measures and the d-Choquet integrals to assess their respective impacts and sensitivities. Finally, the results regarding the classification problem are examined with performance metrics such as accuracy, precision, recall, and F1 score.