Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces

Yılmaz Yılmaz, Hacer Bozkurt, Halise Levent, Ümit Çetinkaya and Francisco J. Garcia Pacheco

Journal of Mathematics, 2022, vol. 2022, 1-15

Abstract: It has been shown that the class of fuzzy sets has a quasilinear space structure. In addition, various norms are defined on this class, and it is given that the class of fuzzy sets is a normed quasilinear space with these norms. In this study, we first developed the algebraic structure of the class of fuzzy sets F℠n and gave definitions such as quasilinear independence, dimension, and the algebraic basis in these spaces. Then, with special norms, namely, uq=∫01supx∈uαxqdα1/q where 1≤q≤∞, we stated that F℠n,uq is a complete normed space. Furthermore, we introduced an inner product in this space for the case q=2. The inner product must be in the formu,v=∫01uα,vα K℠ndα=∫01a,b℠ndα  :a∈uα,b∈vα. For u,v∈F℠n. We also proved that the parallelogram law can only be provided in the regular subspace, not in the entire of F℠n. Finally, we showed that a special class of fuzzy number sequences is a Hilbert quasilinear space.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2022/2466817.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2022/2466817.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2466817

DOI: 10.1155/2022/2466817

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().