Tripathy, Binod Chandra; Sarma, Bipul Sequence spaces of fuzzy real numbers defined by Orlicz functions. (English) Zbl 1199.46167 Math. Slovaca 58, No. 5, 621-628 (2008). An Orlicz function \(M\:[0,\infty)\rightarrow [0,\infty)\) is a continuous, convex, non-decreasing function such that \(M(0)=0\) and \(M(x)>0\) for \(x>0\), and \(M(x)\rightarrow \infty \) as \(x\rightarrow \infty \). If the convexity of theOrlicz function \(M\) is replaced by \[ M(x+y)\leq M(x) + M(y), \] then this function is called a modulus function.The authors define the following sequence spaces of fuzzy real numbers defined by an Orlicz function\[ (l_\infty)_F(M) = \left \{(X_k): \sup _{k} M \left (\frac {\bar {d}(X_k,\bar {0})}{\rho }\right)< \infty ,\quad \text{for some}\; \rho >0 \right \}, \]\[ c_F(M) = \left \{(X_k): \lim _{k} M \left (\frac {\bar {d}(X_k,L)}{\rho }\right)=0 ,\quad \text{for some}\; \rho >0\; \text{and}\; L \in R(I)\right \}, \]\[ (c_0)_F(M) = \left \{(X_k): \lim _{k} M \left (\frac {\bar {d}(X_k,\bar {0})}{\rho }\right)=0 ,\quad \text{for some}\; \rho >0 \right \}. \] Reviewer: Ekrem Savas (Istanbul) Cited in 16 Documents MSC: 46S40 Fuzzy functional analysis 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:fuzzy real number; Orlicz function; solid space; symmetric space PDFBibTeX XMLCite \textit{B. C. Tripathy} and \textit{B. Sarma}, Math. Slovaca 58, No. 5, 621--628 (2008; Zbl 1199.46167) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.