Fault-Tolerant Analysis in Smart Agriculture Using Intuitionistic Fuzzy Zero-Divisor Graph

In this paper, we introduce the concept of Intuitionistic Fuzzy Zero-Divisor Graph (IFZDG) by incorporating Fuzzy Zero-Divisor Graph and intuitionistic fuzzy set theory. For the commutative ring [Formula: see text], let [Formula: see text] be the zero-divisor graph whose vertices are non-zero zero-divisors of [Formula: see text]. We explore an algebraic-graph-based approach to fault tolerance using Intuitionistic Fuzzy Zero-Divisor Graphs. Throughout this paper, we denote the Intuitionistic Fuzzy Zero-Divisor Graph (IFZDG) of [Formula: see text] by [Formula: see text].