Linear Diophantine Fuzzy Subspaces of a Vector Space

Madeleine Al-Tahan (), Sarka Hoskova-Mayerova (), Saba Al-Kaseasbeh and Suha Ali Tahhan
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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

Mathematics, 2023, vol. 11, issue 3, 1-9

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.

Keywords: vector space; subspace; linear diophantine fuzzy set (LDFS); LDF subfield; LDF subspace; level subspace (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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