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Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making

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Summary

This study introduces interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets), a novel mathematical tool for handling uncertain data in fields like economics and medical science. It explores their properties and applications in decision-making problems.

Keywords:
Fuzzy setInterval-valued fuzzy rough soft setIntuitionistic fuzzy rough setRough setSoft set

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Area of Science:

  • Decision Sciences
  • Computer Science
  • Mathematics

Background:

  • Classical mathematical methods struggle with real-world uncertain data.
  • Fuzzy sets, rough sets, and soft sets are existing theories for uncertainty, each with limitations.
  • Intuitionistic fuzzy rough sets (IFrough sets) were previously proposed to model uncertainty.

Purpose of the Study:

  • To introduce the novel concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets).
  • To investigate the properties of IVIFS rough approximation operators.
  • To explore basic operations and properties of IVIFS rough sets.

Main Methods:

  • Development of the interval-valued intuitionistic fuzzy soft rough set framework.
  • Analysis of the properties of associated approximation operators.
  • Examination of fundamental set operations and their characteristics.

Main Results:

  • The paper defines IVIFS rough sets and their approximation operators.
  • Key properties of these operators are investigated and established.
  • Basic operations and their behaviors within the IVIFS rough set model are studied.

Conclusions:

  • The proposed IVIFS rough sets offer a new mathematical tool for uncertainty.
  • The study provides a theoretical foundation for IVIFS rough sets and their applications.
  • Demonstrated utility in decision-making problems highlights the practical relevance of this new framework.