Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces

Basit Öğe Kaydı
dc.contributor.authorYilmaz, Yilmaz
dc.contributor.authorBozkurt, Hacer
dc.contributor.authorLevent, Halise
dc.contributor.authorCetinkaya, Uemit
dc.date.accessioned2024-08-04T20:52:13Z
dc.date.available2024-08-04T20:52:13Z
dc.date.issued2022
dc.departmentİnönü Üniversitesien_US
dc.description.abstractt 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 thealgebraic structure of the class of fuzzy setsF(Rn)and gave definitions such as quasilinear independence, dimension, and thealgebraic basis in these spaces. .en, with special norms, namely,?u?q = ( integral(1)(0)(sup(x is an element of[u]alpha)?x?)(q)d alpha)(1/q )where 1 <= q <=infinity, we stated that (F(R-n),?u?(q))is a complete normed space. Furthermore, we introduced an inner product in this space for the case q=2. .e innerproduct must be in the form = integral(1)(0)<[u](alpha),[v](alpha)>(K(Rn))d alpha=integral(1)(0){(Rn)d alpha:a is an element of[u](alpha),b is an element of[v](alpha)}. Foru,v is an element of F(Rn). We alsoproved that the parallelogram law can only be provided in the regular subspace, not in the entire ofF(Rn).Finally, we showed thata special class of fuzzy number sequences is a Hilbert quasilinear space.en_US
dc.identifier.doi10.1155/2022/2466817
dc.identifier.issn2314-4629
dc.identifier.issn2314-4785
dc.identifier.scopus2-s2.0-85135397617en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.urihttps://doi.org/10.1155/2022/2466817
dc.identifier.urihttps://hdl.handle.net/11616/100819
dc.identifier.volume2022en_US
dc.identifier.wosWOS:000835066700002en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherHindawi Ltden_US
dc.relation.ispartofJournal of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject[No Keywords]en_US
dc.titleInner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spacesen_US
dc.typeArticleen_US

Dosyalar

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu