In this study, we investigate the notions of the Wijsman
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2
-statistical convergence, Wijsman
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2
-lacunary statistical convergence, Wijsman strongly
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2
-lacunary convergence, and Wijsman strongly
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2
-Cesàro convergence of double sequence of sets in the intuitionistic fuzzy metric spaces (briefly, IFMS). Also, we give the notions of Wijsman strongly
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2
∗
-lacunary convergence, Wijsman strongly
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2
-lacunary Cauchy, and Wijsman strongly
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2
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-lacunary Cauchy set sequence in IFMS and establish noteworthy results.