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Related Experiment Video

Updated: May 1, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Minimal solution of singular LR fuzzy linear systems.

M Nikuie1, M Z Ahmad2

  • 1Sama Technical and Vocational Training College, Islamic Azad University, Urmia Branch, Urmia, Iran.

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|April 17, 2014
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Summary

This study introduces singular LR fuzzy linear systems, categorizing them into consistent and inconsistent types. It explores using generalized inverses like the Drazin inverse to find minimal solutions for consistent systems.

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Area of Science:

  • Mathematics
  • Fuzzy Mathematics
  • Linear Algebra

Background:

  • Fuzzy linear systems are essential in various scientific fields.
  • Singular systems present unique challenges in finding solutions.
  • Generalized inverses offer methods for solving linear systems.

Purpose of the Study:

  • To introduce and define singular LR fuzzy linear systems.
  • To classify these systems into consistent and inconsistent categories.
  • To investigate the application of generalized inverses in solving singular consistent LR fuzzy linear systems.

Main Methods:

  • Introduction of the singular LR fuzzy linear system.
  • Classification of systems into consistent and inconsistent types.
  • Analysis of Drazin inverse, pseudoinverse, and {1}-inverse capabilities.

Main Results:

  • The paper defines singular LR fuzzy linear systems.
  • Systems are categorized into singular consistent and singular inconsistent types.
  • The effectiveness of generalized inverses in finding minimal solutions for consistent systems is examined.

Conclusions:

  • Singular LR fuzzy linear systems are formally introduced.
  • A clear distinction is made between consistent and inconsistent singular systems.
  • Generalized inverses are shown to be valuable tools for solving specific types of fuzzy linear systems.