Some Properties of Fuzzy Inner Product Space

  • Jehad R. Kider Branch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology
Keywords: Fuzzy inner product space, Fuzzy orthogonal vectors, Fuzzy orthogonal Complement

Abstract

     Our goal in the present paper is to introduce a new type of fuzzy inner product space. After that, to illustrate this notion, some examples are introduced. Then we prove that that every fuzzy inner product space is a fuzzy normed space. We also prove that the cross product of two fuzzy inner spaces is again a fuzzy inner product space. Next, we prove that the fuzzy inner product is a non decreasing function. Finally, if U is a fuzzy complete fuzzy inner product space and D is a fuzzy closed subspace of U, then we prove that U can be written as a direct sum of D and the fuzzy orthogonal complement    of D.

Published
2021-07-31
How to Cite
Kider, J. R. (2021). Some Properties of Fuzzy Inner Product Space. Iraqi Journal of Science, (7), 2384-2392. https://doi.org/10.24996/ijs.2021.62.7.28
Section
Mathematics