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Soft ordered double quantitative approximations based three-way decisions and their applications.

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Summary
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This study introduces a soft dominance rough set model for incomplete information systems, enhancing multigranulation approaches. The model effectively addresses complex decision-making problems, such as selecting COVID-19 treatments.

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Area of Science:

  • Rough Set Theory
  • Decision Making
  • Incomplete Information Systems

Background:

  • Classical rough set theory uses single equivalence relations, limiting problem-solving capabilities.
  • Multigranulation rough sets handle distributed data but require enhanced models.
  • Incomplete information systems present challenges for traditional set approximation methods.

Purpose of the Study:

  • To develop a soft dominance rough set model for incomplete information systems.
  • To introduce novel multigranulation decision theoretic rough approximations.
  • To apply the proposed model to multi-attribute decision-making problems, specifically COVID-19 treatment selection.

Main Methods:

  • Development of soft preference and soft dominance relations.
  • Analysis of structural properties of the soft dominance rough set model.
  • Introduction of logical disjunction/conjunction soft dominance optimistic/pessimistic multigranulation decision theoretic rough approximations.
  • Formulation of a decision-making algorithm for practical application.

Main Results:

  • The soft dominance rough set model in incomplete information systems yields a maximum of six distinct sets for approximation.
  • Relationships among these six sets are established, defining their structural properties.
  • The proposed multigranulation decision theoretic rough approximations offer a robust framework for uncertainty measurement.
  • A novel decision-making approach is presented for multi-attribute problems.

Conclusions:

  • The soft dominance rough set model provides an effective framework for handling incomplete information.
  • The developed multigranulation decision theoretic rough approximations enhance decision-making capabilities in complex scenarios.
  • The model demonstrates practical applicability in medical diagnosis and treatment selection for diseases like COVID-19.