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Linear Diophantine Fuzzy Subspaces of a Vector Space

Author

Listed:
  • Madeleine Al-Tahan

    (Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi P.O. Box 15551, United Arab Emirates)

  • Sarka Hoskova-Mayerova

    (Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, 662 10 Brno, Czech Republic)

  • Saba Al-Kaseasbeh

    (Department of Mathematics, College of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan)

  • Suha Ali Tahhan

    (Faculty of Business, Lebanese International University, Beirut P.O. Box 146404, Lebanon)

Abstract

The notion of a linear diophantine fuzzy set as a generalization of a fuzzy set is a mathematical approach that deals with vagueness in decision-making problems. The use of reference parameters associated with validity and non-validity functions in linear diophantine fuzzy sets makes it more applicable to model vagueness in many real-life problems. On the other hand, subspaces of vector spaces are of great importance in many fields of science. The aim of this paper is to combine the two notions. In this regard, we consider the linear diophantine fuzzification of a vector space by introducing and studying the linear diophantine fuzzy subspaces of a vector space. First, we studied the behaviors of linear diophantine fuzzy subspaces of a vector space under a linear diophantine fuzzy set. Second, and by means of the level sets, we found a relationship between the linear diophantine fuzzy subspaces of a vector space and the subspaces of a vector space. Finally, we discuss the linear diophantine fuzzy subspaces of a quotient vector space.

Suggested Citation

  • Madeleine Al-Tahan & Sarka Hoskova-Mayerova & Saba Al-Kaseasbeh & Suha Ali Tahhan, 2023. "Linear Diophantine Fuzzy Subspaces of a Vector Space," Mathematics, MDPI, vol. 11(3), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:503-:d:1038942
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    References listed on IDEAS

    as
    1. Ghulam Muhiuddin & Madeline Al-Tahan & Ahsan Mahboob & Sarka Hoskova-Mayerova & Saba Al-Kaseasbeh, 2022. "Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI -Algebras," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
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