Open AccessSome Properties of Fuzzy Inner Product Space
Author(s) -
Jehad R. Kider
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.7.28
Subject(s) - inner product space , mathematics , fuzzy logic , product (mathematics) , fuzzy number , space (punctuation) , fuzzy set operations , complement (music) , subspace topology , fuzzy classification , pure mathematics , fuzzy set , computer science , mathematical analysis , artificial intelligence , geometry , biochemistry , chemistry , complementation , gene , phenotype , operating system
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.