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Algebraic Hyperstructures of Vague Soft Sets Associated with Hyperrings and Hyperideals.

Ganeshsree Selvachandran1, Abdul Razak Salleh2

  • 1Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Jalan Menara Gading, Cheras, 56000 Kuala Lumpur, Malaysia.

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Summary

This study introduces vague soft hyperrings and related concepts by extending classical hyperring theory to vague soft sets. It explores their properties and connections to existing hyperring theories.

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Area of Science:

  • Abstract Algebra
  • Fuzzy Set Theory
  • Soft Set Theory

Background:

  • Hyperring theory provides a generalization of ring theory with applications in abstract algebra.
  • Vague set theory and soft set theory offer frameworks for handling uncertainty and imprecision.
  • Integrating these theories can lead to novel algebraic structures for complex data.

Purpose of the Study:

  • To introduce and define vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphisms.
  • To investigate the fundamental properties and structural characteristics of these new concepts.
  • To establish the relationships between vague soft hyperrings and existing hyperring structures.

Main Methods:

  • Application of classical hyperring theory to the domain of vague soft sets.
  • Development of definitions for vague soft hyperrings, hyperideals, and homomorphisms.
  • Analysis of algebraic properties and structural features.

Main Results:

  • Formalization of vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphisms.
  • Detailed examination of the properties and structural characteristics of these novel concepts.
  • Investigation into the connections between the proposed structures and classical/soft hyperring theories.

Conclusions:

  • The study successfully extends hyperring theory to vague soft sets, creating new algebraic structures.
  • The introduced concepts offer a robust framework for analyzing imprecise and uncertain information within an algebraic context.
  • This work bridges vague set theory, soft set theory, and hyperring theory, opening avenues for future research.