In this paper, we use the notion of ideal convergence (I-convergence) to introduce Tribonacci I-convergent sequence spaces, that is, c I 0 (T), c I (T) and l I ∞ (T) as a domain of regular Tribonacci matrix T = (t jn) (constructed by the Tribonacci sequence). We also present few inclusion relations and prove some topological and algebraic properties based results with respect to these spaces.

The concept of regular matrix was introduced by Wilansky which was later used to define regular Tribonacci matrix by Yaying and Hazarika. In this paper, by using the domain of regular Tribonacci matrix A = (ajk ) and the concept of ideal convergence, we introduce some intuitionistic fuzzy Tribonacci ideal convergent spaces. We also focus on some topological and algebraic properties of these convergent sequence spaces.

In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝ n and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.