Convergence analysis of intuitionistic fuzzy matrices with nearly monotone increasing property

Abstract

Intuitionistic fuzzy matrix convergence of powers has been studied in the literature. The essential role of the main diagonal elements in the convergence of the power sequence of an intuitionistic fuzzy matrix A is exported at the level of A itself by introducing a new classification. The established theorems cover intuitionistic fuzzy matrices that increase monotonically. For matrices of this type, the convergence index is always smaller than or equal to n. The results are more essential because they lay the foundation for the convergence and oscillation of the power sequence of any intuitionistic fuzzy matrix. On the one hand, the results may be seen as a generalization of the results obtained by certain authors. Furthermore, as a typical case to consider, the necessary and sufficient conditions for an increasing intuitionistic fuzzy matrix A to have the property Aⁿ⁻¹ < Aⁿ = Aⁿ⁺ˡ were established.