A study on Riesz I-convergence in intuitionistic fuzzy normed spaces

Khan V. A., SAVAŞ E., Khan I. A., Rahman Z.

Italian Journal of Pure and Applied Mathematics, no.49, pp.771-789, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Journal Name: Italian Journal of Pure and Applied Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Compendex, zbMATH
  • Page Numbers: pp.771-789
  • Keywords: I-Cauchy, I-convergence, intuitionistic fuzzy normed space, Riesz matrix
  • Uşak University Affiliated: Yes

Abstract

The primary objective of this study is to introduce the concept of ideal convergent sequences as a domain of regular Riesz triangular matrix in the settings of intuitionistic fuzzy normed spaces(IFNS). Some properties of this notion with respect to the intuitionistic fuzzy norm are also presented in this study. We demonstrate the Riesz ideal Cauchy criterion in intuitionistic fuzzy normed spaces and later on, we show that in an arbitrary IFNS, a sequence is Riesz ideal convergent if and only if it satisfies Riesz ideal Cauchy criterion. We also present major counterexamples for the converse part of some results. Lastly, we define the notion of Riesz I*-convergence in intuitionistic fuzzy normed spaces and establish the relationship with Riesz I-convergence in IFNS with a certain counterexample.