Enhancing data-driven three-way decision models for incomplete multiscale data: Integrating rough set theory with circular Pythagorean fuzzy rough information for advanced risk assessment


Kamran M., Zhang Q., Jana C., Tahir M., Ivkovic N., PAMUCAR D.

Engineering Applications of Artificial Intelligence, vol.163, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 163
  • Publication Date: 2026
  • Doi Number: 10.1016/j.engappai.2025.112990
  • Journal Name: Engineering Applications of Artificial Intelligence
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Keywords: Circular Pythagorean fuzzy set, Conditional probability, Industry 5.0, Rough set, Three way decision
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The advancement of Industry 5.0 brings unprecedented challenges and complexities in transportation and mobility systems, demanding robust and adaptive risk assessment frameworks. Traditional rough set theory examines how decision-makers respond to risks based on psychological behaviors and preferences, while three-way decision (3-WD) theory provides a structured approach to managing uncertainty through acceptance, rejection, or deferment actions. However, current methods often struggle with incomplete, multiscale data and vague failure information. In response, this study introduces a novel data-driven 3-WD model that integrates rough set theory (RST) with circular Pythagorean fuzzy sets (Cir-PyFSs) to handle missing utility values and ambiguous information in high-stakes environments. Cir-PyFSs capture membership, non-membership, and radius information, offering enhanced flexibility and precision in modeling uncertainty. The proposed model incorporates decision-theoretic rough sets (DTRSs) with a relative loss function framework, effectively addressing unexpected uncertainties and cost-sensitive decisions. To demonstrate its applicability, we present a multi-attribute decision-making (MADM) model based on newly developed operators within Cir-PyFSs settings. Our approach is applied to a real-world transportation and mobility scenario, evaluating the risks and impacts associated with Industry 5.0 adoption. The findings reveal that the proposed model provides a powerful and practical tool for advanced risk assessment, enabling Industry leaders and policymakers to make informed, resilient decisions in rapidly evolving industrial landscapes.