The concept of fuzzy sets was introduced by Zadeh as a means of representing data that was not precise but rather fuzzy. Recently, Koinac [12] studied some topological properties of fuzzy antinormed linear spaces. This has motivated us to introduce and study the fuzzy antinormed double sequence spaces with respect to ideal by using a compact linear operator and prove some theorems, in particular convergence and completeness theorems on these new double sequence spaces.
KhanV.A., Yasmeen, EsiA. and FatimaH., Intuitionistic fuzzy I-convergent double sequence spaces defined by compact operator and modulus function, Journal of Intelligent and Fuzzy Systems33(6) (2017), 3905–3911.
11.
KhanV.A., ShafiqM., Lafuerza-GuillenB., On paranorm}-convergent sequence spaces defined by a compact operator, Afrika Matematika25(4) (2014), 12. DOI 10.1007/s13370-014-0287-2.
12.
KočinacL.J.D.R., Some topological properties of fuzzy antinormed linear spaces, Journal of Mathematics2018, 6. Article ID 9758415. DOI 10.1155/2018-9758415.
13.
KočinacL.J.D.R. and RashidM., On ideal convergence of double sequencea in the topology induced by a fuzzy 2-norm, TWMS Journal of Pure and Applied Mathematics8(1) (2017), 97–111.
14.
KostyrkoP., SalatT., WilczynskiW., I-convergence, Real Analysis Exchange26(2) (2000), 669–686.
15.
MohiuddineS.A., Alotaibi and AlsulamiS.M., Ideal convergence of double sequences in random 2-normd spaces, Advances in Difference Equations2012 (2012), 8. article 149.
16.
MursaleenM., EdelyO.H.H., Statistical convergence of double sequences, Journal of Mathematical Analysis and Applications288 (2003), 223–231.
17.
MursaleenM., MohiuddineS.A., On ideal convergence of double sequences in probabilistic normed spaces, Mathematical Reports12(62) (2010), 359–371.
18.
RashidM., KočinacL.JD.R., Ideal convergence in 2-fuzzy 2-normed spaces, Hacettepe Journal of Mathematics and Statistics46(1) (2017), 149–162.
19.
SasdatiR., VaezpourS.M., Some results of fuzzy Banach spaces, Journal of Applied Mathematics and Computing17 (2005), 475–484.
20.
SchoenbergI.J., The integrability of certain functions and related summability methods, American Mathematical Monthly66 (1959), 361–375.
21.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
