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Setting Limits on Supersymmetry Using Simplified Models
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Fuzzy upper bounds in groupoids.

Sun Shin Ahn1, Young Hee Kim2, J Neggers3

  • 1Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea.

Thescientificworldjournal
|July 2, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces fuzzy upper bounds and either-or subsets within groupoids. Properties of these fuzzy sets and their applications in Bin(X) are explored, enhancing algebraic structure understanding.

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Area of Science:

  • Algebraic Structures
  • Fuzzy Set Theory
  • Mathematical Logic

Background:

  • Groupoids are fundamental algebraic structures.
  • Fuzzy set theory extends classical set theory to handle uncertainty.
  • Existing research lacks comprehensive study of fuzzy bounds in groupoids.

Purpose of the Study:

  • Introduce and investigate fuzzy upper bounds in groupoids.
  • Define and analyze either-or and strong either-or subsets.
  • Explore fuzzy-d-subsets and their properties within groupoid structures.

Main Methods:

  • Formal definition of fuzzy upper bounds over groupoids.
  • Development of definitions for either-or and strong either-or subsets.
  • Investigation of properties within the collection of all groupoids, Bin(X).

Main Results:

  • Established properties of fuzzy upper bounds.
  • Characterized either-or and strong either-or subsets.
  • Introduced and analyzed fuzzy-d-subsets of groupoids.

Conclusions:

  • The study provides a foundational framework for fuzzy concepts in groupoids.
  • The introduced notions offer new tools for analyzing algebraic structures.
  • Further research can extend these concepts to other algebraic systems.