直观模糊赋范空间中双指标序列的收敛性(英文)

Convergence of double-indexed sequences in an intuitionistic fuzzy normed space

目的研究直观模糊赋范空间中双指标序列的收敛性,证明直观模糊赋范空间中的加法、数乘及观模糊范数的连续性。方法定义直观模糊赋范空间中双指标序列的收敛性及有界性。结果证明直观模糊赋范空间中的加法、数乘及直观模糊范数关于双指标序列的连续性。结论本文结果说明了直观模糊赋范空间中的代数结构与拓扑结构是相容的。

Aim To discuss the convergence of double-indexed sequences in an intuitionistic fuzzy normed space（IFNS） and prove that the addition,scalar multiplication and intuitionistic fuzzy norm of double-indexed sequence in an IFNS are all statistically continuous.Methods By introducing the boundedness and convergence of double-indexed sequences in an IFNS,the aforesaid aim is discussed.Results The results are obtained that the addition,scalar multiplication and intuitionistic fuzzy norm of double-indexed sequence in an IFNS are all statistically continuous.Conclusion The result shows that the topological and algebraic structures in an IFNS are compatible.