Document Type : Article
Jaypee University of Information Technology, Waknaghat, Solan, Pin-173 234, Himachal Pradesh, India
Indian Institute of Management Lucknow, Noida Campus, Noida, Pin-201 309, Uttar Pradesh, India
The application problems in the field of pattern recognition, clustering, and knowledge-based expert systems contain a lot of uncertainty in the form of imprecise, incomplete, and inexact information. These decision-making processes well utilize the notions of entropy, discriminant measure, and similarity measure which play a crucial role in the determination. In the present communication, a very recently proposed bi-parametric ($R$, $S$)-norm discriminant measure for picture fuzzy sets has been utilized and different important properties have been discussed. The bi-parametric discriminant measure would give diversification in handling the inexact/incomplete information in terms of obtaining the degree of association and closeness in the data of various applications. The monotonicity of the newly presented discriminant measure in relation to the involved parameters $R$ and $S$ has also been discussed in detail along with its empirical proof. Further, the bi-parametric measure under consideration has been successfully applied in the principle of minimum discriminant information with the help of some illustrative numerical applications in the field of pattern recognition/clustering, etc. Additionally, for the validity and efficacy of the presented approach, necessary and detailed comparison studies along with important findings, advantages, and limitations have been mentioned.