Decision algorithms of fuzzy soft sets and their applications

This thesis addresses the inadequacy of the certainty assumption of classical set theory in modeling uncertain and complex problems in real life; it examines fuzzy set theory and its various generalizations, which were developed to overcome this deficiency. The study first covers the fundamental concepts, membership functions, and basic operations of fuzzy sets, followed by an explanation of α-cuts and their application areas. Subsequently, rough set theory is introduced, demonstrating how uncertain information can be represented using lower and upper approaches. Interval-valued fuzzy sets, heuristic fuzzy sets, and Pythagorean fuzzy sets are also discussed in detail, highlighting their advantages in problems involving uncertainty, hesitation, and decision-making. The final section of the thesis examines soft sets and fuzzy soft sets, illustrating their advantages in parameter-based decision-making processes with examples. Overall, the study aims to demonstrate the effectiveness of modern set theory approaches in solving problems involving uncertainty.