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Invariant convergent and invariant ideal convergent sequence in intuitionistic fuzzy normed space
(IOS Press, 2022) Khan, Vakeel A.; Ali Khan, Izhar; Esi, Ayhan; Alam, Masood
The main purpose of this paper is to introduce invariant convergence in intuitionistic fuzzy normed space. Following which we present some characteristics of this notion with respect to intuitionistic fuzzy norm. We also define strongly invariant convergence, ideal invariant convergence and invariant ideal convergence in intuitionistic fuzzy normed space. After that, we establish the relationship between these notions with respect to intuitionistic fuzzy norm. Lastly, we define ideal invariant Cauchy and invariant ideal Cauchy criteria for sequences in intuitionistic fuzzy normed space and relate it to their convergence notion.
Some results on wijsman ideal convergence in intuitionistic fuzzy metric spaces
(Hindawi, 2020) Esi, Ayhan; Khan, Vakeel Ahmad; Ahmad, Mobeen; Alam, Masood
In the present work, we study and extend the notion of Wijsman J-convergence and Wijsman J*-convergence for the sequence of closed sets in a more general setting, i.e., in the intuitionistic fuzzy metric spaces (briefly, IFMS). Furthermore, we also examine the concept of Wijsman J*-Cauchy and J-Cauchy sequence in the intuitionistic fuzzy metric space and observe some properties.