Notes on soft sets and aggregation operators

Abstract

[EN]Under uncertainty, traditional sets may not be sufficient to represent real-world phenomena, and fuzzy sets can provide a more flexible and natural approach. The concept of fuzzy sets has been widely used in various fields, including artificial intelligence, control theory, decision-making, and pattern recognition. Fuzzy sets can also be combined with other mathematical tools, such as probability theory, to provide a more comprehensive approach to uncertainty management. In these notes, we explore the concept of fuzzy sets under uncertainty, and their applications in various fields. We discuss the fundamental concepts of fuzzy sets, including fuzzy membership functions, fuzzy operations, and fuzzy relations. We also examine different types of uncertainty, including epistemic and aleatory uncertainty, and how fuzzy sets can be used to model and manage uncertainty in these cases.