Intuitionistic Fuzzy Binary Soft Sets and Its Properties

Objective : The objective of Intuitionistic fuzzy binary soft sets is to extend the existing frameworks of binary soft sets and Intuitionistic fuzzy sets to accommodate both uncertainty and ambiguity in decision-making processes. This extension aims to provide a more flexible, representation of real-world data and phenomena, allowing for analysis and reasoning. Specifically, the objective involves defining the fundamental structures of Intuitionistic fuzzy binary soft sets over two initial universal sets, U1 and U2. Method: Reviewing the existing literature on binary soft sets, Intuitionistic fuzzy sets, and their extensions. Defining the fundamental structures of Intuitionistic fuzzy binary soft sets over two initial universal sets, U1 and U2. The next step is to propose the operations on Intuitionistic fuzzy binary soft sets and analyze their characteristics. Findings: The extension of binary soft sets and Intuitionistic fuzzy sets to Intuitionistic fuzzy binary soft sets is feasible. Intuitionistic fuzzy binary soft sets possess distinct properties worthy of exploration. Operations such as union, intersection, difference, AND, Or of Intuitionistic fuzzy binary soft sets exhibit specific behaviors elucidated through our findings. Novelty: The development of operations on Intuitionistic fuzzy binary soft sets provides a comprehensive framework and analysis. Exploration of properties unique to Intuitionistic fuzzy binary soft sets is contributing to the advancement of soft computing and set theory. Mathematics Classification code: 03D45, 03F55, 03E72 Keywords: Fuzzy, Soft, Intuitionistic, Binary soft, Fuzzy binary soft