In this paper, we study the concepts of Wijsman lacunary \({\mathcal{I}}\)-invariant convergence \(\left( {{\mathcal{I}}_{\sigma \theta }^{W} } \right),\) Wijsman lacunary \({\mathcal{I}}^{ *}\)-invariant convergence \(\left( {{\mathcal{I}}_{\sigma \theta }^{ *W} } \right),\) Wijsman \(p\)-strongly lacunary invariant convergence \(\left( {[WN_{\sigma \theta } ]_{p} } \right)\) of sequences of sets and investigate the relationships among Wijsman lacunary invariant convergence, \([WN_{\sigma \theta } ]_{p}\), \({\mathcal{I}}_{\sigma \theta }^{W}\) and \({\mathcal{I}}_{\sigma \theta }^{ *W}\). Also, we introduce the concepts of \({\mathcal{I}}_{\sigma \theta }^{W}\)-Cauchy sequence and \({\mathcal{I}}_{\sigma \theta }^{ *W}\)-Cauchy sequence of sets.

在本文中，我们研究了Wijsman词法\（{\ mathcal {I}} \）-不变收敛\（\ left（{{\ mathcal {I}} _ {\ sigma \ theta} ^ {W}}的概念\ right），\） Wijsman腔（\ {{\ mathcal {I}} ^ {*} \）-不变收敛\（\ left（{{\ mathcal {I}} _ {\ sigma \ theta} ^ {* W }} \右），\） Wijsman \（p \） -strongly缺位不变收敛\（\左（{[WN _ {\西格玛\ THETA}] _ {p}} \右）\）的序列集，并调查Wijsman恒常不变收敛，\（[WN _ {\ sigma \ theta}] _ {p} \），\（{\ mathcal {I}} _ {\ sigma \ theta} ^ {W} \）和\之间的关系（{\ mathcal {I}} _ {\ sigma \ theta} ^ {* W} \）。此外，我们介绍了\（{\ mathcal {I}} _ {\ sigma \ theta} ^ {W} \）-漂亮序列和\（{\ mathcal {I}} _ {\ sigma \ theta} ^的概念{* W} \） -集的模糊序列。